[{"data":1,"prerenderedAt":3900},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fleibniz-kriterium":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fleibniz-kriterium":3890},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":555,"category":412,"checks":3816,"conditions":3848,"conditionsHtml":3849,"deprecated":3850,"description":3810,"extension":3851,"figure":3850,"figureCaption":3850,"figureHtml":3850,"formulaId":3852,"latex":3853,"latexHtml":3854,"level":3855,"meta":3856,"navigation":3857,"path":3858,"redirectFrom":3859,"related":3860,"seo":3864,"stem":3865,"subject":585,"summary":3866,"tags":3867,"variables":3872,"__hash__":3889},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fleibniz-kriterium.md","Leibniz-Kriterium",[550,551,552,553,554],"Leibnizkriterium","Konvergenz alternierender Reihen","alternierende Reihe Konvergenz","Leibniz-Reihe","alternierende harmonische Reihe",{"type":556,"value":557,"toc":3809},"minimark",[558,563,686,947,958,993,997,1507,1985,2192,3144,3627,3631],[559,560,562],"h2",{"id":561},"erklärung","Erklärung",[564,565,566,567,571,572,574,575,681,682,685],"p",{},"Eine Reihe heißt ",[568,569,570],"strong",{},"alternierend",", wenn ihre Glieder abwechselnd positiv und negativ sind. Das ",[568,573,548],{}," sagt: Bilden die Beträge ",[576,577,580,609],"span",{"className":578},[579],"katex",[576,581,584],{"className":582},[583],"katex-mathml",[585,586,588],"math",{"xmlns":587},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[589,590,591,604],"semantics",{},[592,593,594],"mrow",{},[595,596,597,601],"msub",{},[598,599,600],"mi",{},"a",[598,602,603],{},"n",[605,606,608],"annotation",{"encoding":607},"application\u002Fx-tex","a_n",[576,610,614],{"className":611,"ariaHidden":613},[612],"katex-html","true",[576,615,618,623],{"className":616},[617],"base",[576,619],{"className":620,"style":622},[621],"strut","height:0.5806em;vertical-align:-0.15em;",[576,624,627,631],{"className":625},[626],"mord",[576,628,600],{"className":629},[626,630],"mathnormal",[576,632,635],{"className":633},[634],"msupsub",[576,636,640,672],{"className":637},[638,639],"vlist-t","vlist-t2",[576,641,644,667],{"className":642},[643],"vlist-r",[576,645,649],{"className":646,"style":648},[647],"vlist","height:0.1514em;",[576,650,652,657],{"style":651},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[576,653],{"className":654,"style":656},[655],"pstrut","height:2.7em;",[576,658,664],{"className":659},[660,661,662,663],"sizing","reset-size6","size3","mtight",[576,665,603],{"className":666},[626,630,663],[576,668,671],{"className":669},[670],"vlist-s","​",[576,673,675],{"className":674},[643],[576,676,679],{"className":677,"style":678},[647],"height:0.15em;",[576,680],{}," eine ",[568,683,684],{},"monoton fallende Nullfolge",", dann konvergiert die alternierende Reihe.",[564,687,688,689,719,720,723,724,752,753,823,824,917,918,946],{},"Die Partialsummen springen dabei abwechselnd über und unter den Grenzwert ",[576,690,692,706],{"className":691},[579],[576,693,695],{"className":694},[583],[585,696,697],{"xmlns":587},[589,698,699,704],{},[592,700,701],{},[598,702,703],{},"s",[605,705,703],{"encoding":607},[576,707,709],{"className":708,"ariaHidden":613},[612],[576,710,712,716],{"className":711},[617],[576,713],{"className":714,"style":715},[621],"height:0.4306em;",[576,717,703],{"className":718},[626,630],", und die Sprünge werden immer kleiner. Daraus folgt die ",[568,721,722],{},"Fehlerabschätzung",": Der Abstand zwischen ",[576,725,727,740],{"className":726},[579],[576,728,730],{"className":729},[583],[585,731,732],{"xmlns":587},[589,733,734,738],{},[592,735,736],{},[598,737,703],{},[605,739,703],{"encoding":607},[576,741,743],{"className":742,"ariaHidden":613},[612],[576,744,746,749],{"className":745},[617],[576,747],{"className":748,"style":715},[621],[576,750,703],{"className":751},[626,630]," und ",[576,754,756,774],{"className":755},[579],[576,757,759],{"className":758},[583],[585,760,761],{"xmlns":587},[589,762,763,771],{},[592,764,765],{},[595,766,767,769],{},[598,768,703],{},[598,770,603],{},[605,772,773],{"encoding":607},"s_n",[576,775,777],{"className":776,"ariaHidden":613},[612],[576,778,780,783],{"className":779},[617],[576,781],{"className":782,"style":622},[621],[576,784,786,789],{"className":785},[626],[576,787,703],{"className":788},[626,630],[576,790,792],{"className":791},[634],[576,793,795,815],{"className":794},[638,639],[576,796,798,812],{"className":797},[643],[576,799,801],{"className":800,"style":648},[647],[576,802,803,806],{"style":651},[576,804],{"className":805,"style":656},[655],[576,807,809],{"className":808},[660,661,662,663],[576,810,603],{"className":811},[626,630,663],[576,813,671],{"className":814},[670],[576,816,818],{"className":817},[643],[576,819,821],{"className":820,"style":678},[647],[576,822],{}," ist höchstens so groß wie das erste weggelassene Glied ",[576,825,827,855],{"className":826},[579],[576,828,830],{"className":829},[583],[585,831,832],{"xmlns":587},[589,833,834,852],{},[592,835,836],{},[595,837,838,840],{},[598,839,600],{},[592,841,842,844,848],{},[598,843,603],{},[845,846,847],"mo",{},"+",[849,850,851],"mn",{},"1",[605,853,854],{"encoding":607},"a_{n+1}",[576,856,858],{"className":857,"ariaHidden":613},[612],[576,859,861,865],{"className":860},[617],[576,862],{"className":863,"style":864},[621],"height:0.6389em;vertical-align:-0.2083em;",[576,866,868,871],{"className":867},[626],[576,869,600],{"className":870},[626,630],[576,872,874],{"className":873},[634],[576,875,877,908],{"className":876},[638,639],[576,878,880,905],{"className":879},[643],[576,881,884],{"className":882,"style":883},[647],"height:0.3011em;",[576,885,886,889],{"style":651},[576,887],{"className":888,"style":656},[655],[576,890,892],{"className":891},[660,661,662,663],[576,893,895,898,902],{"className":894},[626,663],[576,896,603],{"className":897},[626,630,663],[576,899,847],{"className":900},[901,663],"mbin",[576,903,851],{"className":904},[626,663],[576,906,671],{"className":907},[670],[576,909,911],{"className":910},[643],[576,912,915],{"className":913,"style":914},[647],"height:0.2083em;",[576,916],{},". Außerdem liegt ",[576,919,921,934],{"className":920},[579],[576,922,924],{"className":923},[583],[585,925,926],{"xmlns":587},[589,927,928,932],{},[592,929,930],{},[598,931,703],{},[605,933,703],{"encoding":607},[576,935,937],{"className":936,"ariaHidden":613},[612],[576,938,940,943],{"className":939},[617],[576,941],{"className":942,"style":715},[621],[576,944,703],{"className":945},[626,630]," immer zwischen zwei aufeinanderfolgenden Partialsummen.",[564,948,949,950,953,954,957],{},"Das Kriterium zeigt nur Konvergenz, nicht ",[568,951,952],{},"absolute"," Konvergenz. Die alternierende harmonische Reihe konvergiert, die Reihe der Beträge (die harmonische Reihe) aber nicht. Solche Reihen heißen ",[568,955,956],{},"bedingt konvergent","; ihre Glieder darf man nicht beliebig umordnen.",[564,959,960,961,992],{},"Beginnt die Reihe mit einem negativen Glied oder bei einem anderen Index, gilt dasselbe. Monotonie muss erst ab einem Index ",[576,962,964,978],{"className":963},[579],[576,965,967],{"className":966},[583],[585,968,969],{"xmlns":587},[589,970,971,976],{},[592,972,973],{},[598,974,975],{},"N",[605,977,975],{"encoding":607},[576,979,981],{"className":980,"ariaHidden":613},[612],[576,982,984,988],{"className":983},[617],[576,985],{"className":986,"style":987},[621],"height:0.6833em;",[576,989,975],{"className":990,"style":991},[626,630],"margin-right:0.109em;"," gelten.",[559,994,996],{"id":995},"beispiele","Beispiele",[564,998,999,1000,1002,1003,1258,1259,1423,1424,1506],{},"Die ",[568,1001,554],{}," ",[576,1004,1006,1045],{"className":1005},[579],[576,1007,1009],{"className":1008},[583],[585,1010,1011],{"xmlns":587},[589,1012,1013,1042],{},[592,1014,1015,1017,1020,1028,1030,1037,1039],{},[849,1016,851],{},[845,1018,1019],{},"−",[1021,1022,1023,1025],"mfrac",{},[849,1024,851],{},[849,1026,1027],{},"2",[845,1029,847],{},[1021,1031,1032,1034],{},[849,1033,851],{},[849,1035,1036],{},"3",[845,1038,1019],{},[845,1040,1041],{},"…",[605,1043,1044],{"encoding":607},"1 - \\frac{1}{2} + \\frac{1}{3} - \\ldots",[576,1046,1048,1069,1164,1247],{"className":1047,"ariaHidden":613},[612],[576,1049,1051,1055,1058,1063,1066],{"className":1050},[617],[576,1052],{"className":1053,"style":1054},[621],"height:0.7278em;vertical-align:-0.0833em;",[576,1056,851],{"className":1057},[626],[576,1059],{"className":1060,"style":1062},[1061],"mspace","margin-right:0.2222em;",[576,1064,1019],{"className":1065},[901],[576,1067],{"className":1068,"style":1062},[1061],[576,1070,1072,1076,1155,1158,1161],{"className":1071},[617],[576,1073],{"className":1074,"style":1075},[621],"height:1.1901em;vertical-align:-0.345em;",[576,1077,1079,1084,1151],{"className":1078},[626],[576,1080],{"className":1081},[1082,1083],"mopen","nulldelimiter",[576,1085,1087],{"className":1086},[1021],[576,1088,1090,1142],{"className":1089},[638,639],[576,1091,1093,1139],{"className":1092},[643],[576,1094,1097,1113,1124],{"className":1095,"style":1096},[647],"height:0.8451em;",[576,1098,1100,1104],{"style":1099},"top:-2.655em;",[576,1101],{"className":1102,"style":1103},[655],"height:3em;",[576,1105,1107],{"className":1106},[660,661,662,663],[576,1108,1110],{"className":1109},[626,663],[576,1111,1027],{"className":1112},[626,663],[576,1114,1116,1119],{"style":1115},"top:-3.23em;",[576,1117],{"className":1118,"style":1103},[655],[576,1120],{"className":1121,"style":1123},[1122],"frac-line","border-bottom-width:0.04em;",[576,1125,1127,1130],{"style":1126},"top:-3.394em;",[576,1128],{"className":1129,"style":1103},[655],[576,1131,1133],{"className":1132},[660,661,662,663],[576,1134,1136],{"className":1135},[626,663],[576,1137,851],{"className":1138},[626,663],[576,1140,671],{"className":1141},[670],[576,1143,1145],{"className":1144},[643],[576,1146,1149],{"className":1147,"style":1148},[647],"height:0.345em;",[576,1150],{},[576,1152],{"className":1153},[1154,1083],"mclose",[576,1156],{"className":1157,"style":1062},[1061],[576,1159,847],{"className":1160},[901],[576,1162],{"className":1163,"style":1062},[1061],[576,1165,1167,1170,1238,1241,1244],{"className":1166},[617],[576,1168],{"className":1169,"style":1075},[621],[576,1171,1173,1176,1235],{"className":1172},[626],[576,1174],{"className":1175},[1082,1083],[576,1177,1179],{"className":1178},[1021],[576,1180,1182,1227],{"className":1181},[638,639],[576,1183,1185,1224],{"className":1184},[643],[576,1186,1188,1202,1210],{"className":1187,"style":1096},[647],[576,1189,1190,1193],{"style":1099},[576,1191],{"className":1192,"style":1103},[655],[576,1194,1196],{"className":1195},[660,661,662,663],[576,1197,1199],{"className":1198},[626,663],[576,1200,1036],{"className":1201},[626,663],[576,1203,1204,1207],{"style":1115},[576,1205],{"className":1206,"style":1103},[655],[576,1208],{"className":1209,"style":1123},[1122],[576,1211,1212,1215],{"style":1126},[576,1213],{"className":1214,"style":1103},[655],[576,1216,1218],{"className":1217},[660,661,662,663],[576,1219,1221],{"className":1220},[626,663],[576,1222,851],{"className":1223},[626,663],[576,1225,671],{"className":1226},[670],[576,1228,1230],{"className":1229},[643],[576,1231,1233],{"className":1232,"style":1148},[647],[576,1234],{},[576,1236],{"className":1237},[1154,1083],[576,1239],{"className":1240,"style":1062},[1061],[576,1242,1019],{"className":1243},[901],[576,1245],{"className":1246,"style":1062},[1061],[576,1248,1250,1254],{"className":1249},[617],[576,1251],{"className":1252,"style":1253},[621],"height:0.123em;",[576,1255,1041],{"className":1256},[1257],"minner"," erfüllt die Voraussetzungen mit ",[576,1260,1262,1289],{"className":1261},[579],[576,1263,1265],{"className":1264},[583],[585,1266,1267],{"xmlns":587},[589,1268,1269,1286],{},[592,1270,1271,1277,1280],{},[595,1272,1273,1275],{},[598,1274,600],{},[598,1276,603],{},[845,1278,1279],{},"=",[1021,1281,1282,1284],{},[849,1283,851],{},[598,1285,603],{},[605,1287,1288],{"encoding":607},"a_n = \\frac{1}{n}",[576,1290,1292,1349],{"className":1291,"ariaHidden":613},[612],[576,1293,1295,1298,1338,1342,1346],{"className":1294},[617],[576,1296],{"className":1297,"style":622},[621],[576,1299,1301,1304],{"className":1300},[626],[576,1302,600],{"className":1303},[626,630],[576,1305,1307],{"className":1306},[634],[576,1308,1310,1330],{"className":1309},[638,639],[576,1311,1313,1327],{"className":1312},[643],[576,1314,1316],{"className":1315,"style":648},[647],[576,1317,1318,1321],{"style":651},[576,1319],{"className":1320,"style":656},[655],[576,1322,1324],{"className":1323},[660,661,662,663],[576,1325,603],{"className":1326},[626,630,663],[576,1328,671],{"className":1329},[670],[576,1331,1333],{"className":1332},[643],[576,1334,1336],{"className":1335,"style":678},[647],[576,1337],{},[576,1339],{"className":1340,"style":1341},[1061],"margin-right:0.2778em;",[576,1343,1279],{"className":1344},[1345],"mrel",[576,1347],{"className":1348,"style":1341},[1061],[576,1350,1352,1355],{"className":1351},[617],[576,1353],{"className":1354,"style":1075},[621],[576,1356,1358,1361,1420],{"className":1357},[626],[576,1359],{"className":1360},[1082,1083],[576,1362,1364],{"className":1363},[1021],[576,1365,1367,1412],{"className":1366},[638,639],[576,1368,1370,1409],{"className":1369},[643],[576,1371,1373,1387,1395],{"className":1372,"style":1096},[647],[576,1374,1375,1378],{"style":1099},[576,1376],{"className":1377,"style":1103},[655],[576,1379,1381],{"className":1380},[660,661,662,663],[576,1382,1384],{"className":1383},[626,663],[576,1385,603],{"className":1386},[626,630,663],[576,1388,1389,1392],{"style":1115},[576,1390],{"className":1391,"style":1103},[655],[576,1393],{"className":1394,"style":1123},[1122],[576,1396,1397,1400],{"style":1126},[576,1398],{"className":1399,"style":1103},[655],[576,1401,1403],{"className":1402},[660,661,662,663],[576,1404,1406],{"className":1405},[626,663],[576,1407,851],{"className":1408},[626,663],[576,1410,671],{"className":1411},[670],[576,1413,1415],{"className":1414},[643],[576,1416,1418],{"className":1417,"style":1148},[647],[576,1419],{},[576,1421],{"className":1422},[1154,1083],". Ihr Wert ist ",[576,1425,1427,1453],{"className":1426},[579],[576,1428,1430],{"className":1429},[583],[585,1431,1432],{"xmlns":587},[589,1433,1434,1450],{},[592,1435,1436,1439,1442,1444,1447],{},[598,1437,1438],{},"ln",[845,1440,1441],{},"⁡",[849,1443,1027],{},[845,1445,1446],{},"≈",[849,1448,1449],{},"0,6931",[605,1451,1452],{"encoding":607},"\\ln 2 \\approx 0{,}6931",[576,1454,1456,1483],{"className":1455,"ariaHidden":613},[612],[576,1457,1459,1463,1467,1471,1474,1477,1480],{"className":1458},[617],[576,1460],{"className":1461,"style":1462},[621],"height:0.6944em;",[576,1464,1438],{"className":1465},[1466],"mop",[576,1468],{"className":1469,"style":1470},[1061],"margin-right:0.1667em;",[576,1472,1027],{"className":1473},[626],[576,1475],{"className":1476,"style":1341},[1061],[576,1478,1446],{"className":1479},[1345],[576,1481],{"className":1482,"style":1341},[1061],[576,1484,1486,1490,1494,1502],{"className":1485},[617],[576,1487],{"className":1488,"style":1489},[621],"height:0.8389em;vertical-align:-0.1944em;",[576,1491,1493],{"className":1492},[626],"0",[576,1495,1497],{"className":1496},[626],[576,1498,1501],{"className":1499},[1500],"mpunct",",",[576,1503,1505],{"className":1504},[626],"6931",". Die vierte Partialsumme ist",[576,1508,1511],{"className":1509},[1510],"katex-display",[576,1512,1514,1577],{"className":1513},[579],[576,1515,1517],{"className":1516},[583],[585,1518,1520],{"xmlns":587,"display":1519},"block",[589,1521,1522,1574],{},[592,1523,1524,1531,1533,1535,1537,1543,1545,1551,1553,1559,1561,1569,1571],{},[595,1525,1526,1528],{},[598,1527,703],{},[849,1529,1530],{},"4",[845,1532,1279],{},[849,1534,851],{},[845,1536,1019],{},[1021,1538,1539,1541],{},[849,1540,851],{},[849,1542,1027],{},[845,1544,847],{},[1021,1546,1547,1549],{},[849,1548,851],{},[849,1550,1036],{},[845,1552,1019],{},[1021,1554,1555,1557],{},[849,1556,851],{},[849,1558,1530],{},[845,1560,1279],{},[1021,1562,1563,1566],{},[849,1564,1565],{},"7",[849,1567,1568],{},"12",[845,1570,1446],{},[849,1572,1573],{},"0,5833",[605,1575,1576],{"encoding":607},"s_4 = 1 - \\frac{1}{2} + \\frac{1}{3} - \\frac{1}{4} = \\frac{7}{12} \\approx 0{,}5833",[576,1578,1580,1635,1653,1735,1812,1889,1966],{"className":1579,"ariaHidden":613},[612],[576,1581,1583,1586,1626,1629,1632],{"className":1582},[617],[576,1584],{"className":1585,"style":622},[621],[576,1587,1589,1592],{"className":1588},[626],[576,1590,703],{"className":1591},[626,630],[576,1593,1595],{"className":1594},[634],[576,1596,1598,1618],{"className":1597},[638,639],[576,1599,1601,1615],{"className":1600},[643],[576,1602,1604],{"className":1603,"style":883},[647],[576,1605,1606,1609],{"style":651},[576,1607],{"className":1608,"style":656},[655],[576,1610,1612],{"className":1611},[660,661,662,663],[576,1613,1530],{"className":1614},[626,663],[576,1616,671],{"className":1617},[670],[576,1619,1621],{"className":1620},[643],[576,1622,1624],{"className":1623,"style":678},[647],[576,1625],{},[576,1627],{"className":1628,"style":1341},[1061],[576,1630,1279],{"className":1631},[1345],[576,1633],{"className":1634,"style":1341},[1061],[576,1636,1638,1641,1644,1647,1650],{"className":1637},[617],[576,1639],{"className":1640,"style":1054},[621],[576,1642,851],{"className":1643},[626],[576,1645],{"className":1646,"style":1062},[1061],[576,1648,1019],{"className":1649},[901],[576,1651],{"className":1652,"style":1062},[1061],[576,1654,1656,1660,1726,1729,1732],{"className":1655},[617],[576,1657],{"className":1658,"style":1659},[621],"height:2.0074em;vertical-align:-0.686em;",[576,1661,1663,1666,1723],{"className":1662},[626],[576,1664],{"className":1665},[1082,1083],[576,1667,1669],{"className":1668},[1021],[576,1670,1672,1714],{"className":1671},[638,639],[576,1673,1675,1711],{"className":1674},[643],[576,1676,1679,1691,1699],{"className":1677,"style":1678},[647],"height:1.3214em;",[576,1680,1682,1685],{"style":1681},"top:-2.314em;",[576,1683],{"className":1684,"style":1103},[655],[576,1686,1688],{"className":1687},[626],[576,1689,1027],{"className":1690},[626],[576,1692,1693,1696],{"style":1115},[576,1694],{"className":1695,"style":1103},[655],[576,1697],{"className":1698,"style":1123},[1122],[576,1700,1702,1705],{"style":1701},"top:-3.677em;",[576,1703],{"className":1704,"style":1103},[655],[576,1706,1708],{"className":1707},[626],[576,1709,851],{"className":1710},[626],[576,1712,671],{"className":1713},[670],[576,1715,1717],{"className":1716},[643],[576,1718,1721],{"className":1719,"style":1720},[647],"height:0.686em;",[576,1722],{},[576,1724],{"className":1725},[1154,1083],[576,1727],{"className":1728,"style":1062},[1061],[576,1730,847],{"className":1731},[901],[576,1733],{"className":1734,"style":1062},[1061],[576,1736,1738,1741,1803,1806,1809],{"className":1737},[617],[576,1739],{"className":1740,"style":1659},[621],[576,1742,1744,1747,1800],{"className":1743},[626],[576,1745],{"className":1746},[1082,1083],[576,1748,1750],{"className":1749},[1021],[576,1751,1753,1792],{"className":1752},[638,639],[576,1754,1756,1789],{"className":1755},[643],[576,1757,1759,1770,1778],{"className":1758,"style":1678},[647],[576,1760,1761,1764],{"style":1681},[576,1762],{"className":1763,"style":1103},[655],[576,1765,1767],{"className":1766},[626],[576,1768,1036],{"className":1769},[626],[576,1771,1772,1775],{"style":1115},[576,1773],{"className":1774,"style":1103},[655],[576,1776],{"className":1777,"style":1123},[1122],[576,1779,1780,1783],{"style":1701},[576,1781],{"className":1782,"style":1103},[655],[576,1784,1786],{"className":1785},[626],[576,1787,851],{"className":1788},[626],[576,1790,671],{"className":1791},[670],[576,1793,1795],{"className":1794},[643],[576,1796,1798],{"className":1797,"style":1720},[647],[576,1799],{},[576,1801],{"className":1802},[1154,1083],[576,1804],{"className":1805,"style":1062},[1061],[576,1807,1019],{"className":1808},[901],[576,1810],{"className":1811,"style":1062},[1061],[576,1813,1815,1818,1880,1883,1886],{"className":1814},[617],[576,1816],{"className":1817,"style":1659},[621],[576,1819,1821,1824,1877],{"className":1820},[626],[576,1822],{"className":1823},[1082,1083],[576,1825,1827],{"className":1826},[1021],[576,1828,1830,1869],{"className":1829},[638,639],[576,1831,1833,1866],{"className":1832},[643],[576,1834,1836,1847,1855],{"className":1835,"style":1678},[647],[576,1837,1838,1841],{"style":1681},[576,1839],{"className":1840,"style":1103},[655],[576,1842,1844],{"className":1843},[626],[576,1845,1530],{"className":1846},[626],[576,1848,1849,1852],{"style":1115},[576,1850],{"className":1851,"style":1103},[655],[576,1853],{"className":1854,"style":1123},[1122],[576,1856,1857,1860],{"style":1701},[576,1858],{"className":1859,"style":1103},[655],[576,1861,1863],{"className":1862},[626],[576,1864,851],{"className":1865},[626],[576,1867,671],{"className":1868},[670],[576,1870,1872],{"className":1871},[643],[576,1873,1875],{"className":1874,"style":1720},[647],[576,1876],{},[576,1878],{"className":1879},[1154,1083],[576,1881],{"className":1882,"style":1341},[1061],[576,1884,1279],{"className":1885},[1345],[576,1887],{"className":1888,"style":1341},[1061],[576,1890,1892,1895,1957,1960,1963],{"className":1891},[617],[576,1893],{"className":1894,"style":1659},[621],[576,1896,1898,1901,1954],{"className":1897},[626],[576,1899],{"className":1900},[1082,1083],[576,1902,1904],{"className":1903},[1021],[576,1905,1907,1946],{"className":1906},[638,639],[576,1908,1910,1943],{"className":1909},[643],[576,1911,1913,1924,1932],{"className":1912,"style":1678},[647],[576,1914,1915,1918],{"style":1681},[576,1916],{"className":1917,"style":1103},[655],[576,1919,1921],{"className":1920},[626],[576,1922,1568],{"className":1923},[626],[576,1925,1926,1929],{"style":1115},[576,1927],{"className":1928,"style":1103},[655],[576,1930],{"className":1931,"style":1123},[1122],[576,1933,1934,1937],{"style":1701},[576,1935],{"className":1936,"style":1103},[655],[576,1938,1940],{"className":1939},[626],[576,1941,1565],{"className":1942},[626],[576,1944,671],{"className":1945},[670],[576,1947,1949],{"className":1948},[643],[576,1950,1952],{"className":1951,"style":1720},[647],[576,1953],{},[576,1955],{"className":1956},[1154,1083],[576,1958],{"className":1959,"style":1341},[1061],[576,1961,1446],{"className":1962},[1345],[576,1964],{"className":1965,"style":1341},[1061],[576,1967,1969,1972,1975,1981],{"className":1968},[617],[576,1970],{"className":1971,"style":1489},[621],[576,1973,1493],{"className":1974},[626],[576,1976,1978],{"className":1977},[626],[576,1979,1501],{"className":1980},[1500],[576,1982,1984],{"className":1983},[626],"5833",[564,1986,1987,1988,2028,2029,2191],{},"Der tatsächliche Fehler ",[576,1989,1991,2006],{"className":1990},[579],[576,1992,1994],{"className":1993},[583],[585,1995,1996],{"xmlns":587},[589,1997,1998,2003],{},[592,1999,2000],{},[849,2001,2002],{},"0,1098",[605,2004,2005],{"encoding":607},"0{,}1098",[576,2007,2009],{"className":2008,"ariaHidden":613},[612],[576,2010,2012,2015,2018,2024],{"className":2011},[617],[576,2013],{"className":2014,"style":1489},[621],[576,2016,1493],{"className":2017},[626],[576,2019,2021],{"className":2020},[626],[576,2022,1501],{"className":2023},[1500],[576,2025,2027],{"className":2026},[626],"1098"," ist kleiner als die Schranke ",[576,2030,2032,2059],{"className":2031},[579],[576,2033,2035],{"className":2034},[583],[585,2036,2037],{"xmlns":587},[589,2038,2039,2056],{},[592,2040,2041,2048,2050],{},[595,2042,2043,2045],{},[598,2044,600],{},[849,2046,2047],{},"5",[845,2049,1279],{},[1021,2051,2052,2054],{},[849,2053,851],{},[849,2055,2047],{},[605,2057,2058],{"encoding":607},"a_5 = \\frac{1}{5}",[576,2060,2062,2117],{"className":2061,"ariaHidden":613},[612],[576,2063,2065,2068,2108,2111,2114],{"className":2064},[617],[576,2066],{"className":2067,"style":622},[621],[576,2069,2071,2074],{"className":2070},[626],[576,2072,600],{"className":2073},[626,630],[576,2075,2077],{"className":2076},[634],[576,2078,2080,2100],{"className":2079},[638,639],[576,2081,2083,2097],{"className":2082},[643],[576,2084,2086],{"className":2085,"style":883},[647],[576,2087,2088,2091],{"style":651},[576,2089],{"className":2090,"style":656},[655],[576,2092,2094],{"className":2093},[660,661,662,663],[576,2095,2047],{"className":2096},[626,663],[576,2098,671],{"className":2099},[670],[576,2101,2103],{"className":2102},[643],[576,2104,2106],{"className":2105,"style":678},[647],[576,2107],{},[576,2109],{"className":2110,"style":1341},[1061],[576,2112,1279],{"className":2113},[1345],[576,2115],{"className":2116,"style":1341},[1061],[576,2118,2120,2123],{"className":2119},[617],[576,2121],{"className":2122,"style":1075},[621],[576,2124,2126,2129,2188],{"className":2125},[626],[576,2127],{"className":2128},[1082,1083],[576,2130,2132],{"className":2131},[1021],[576,2133,2135,2180],{"className":2134},[638,639],[576,2136,2138,2177],{"className":2137},[643],[576,2139,2141,2155,2163],{"className":2140,"style":1096},[647],[576,2142,2143,2146],{"style":1099},[576,2144],{"className":2145,"style":1103},[655],[576,2147,2149],{"className":2148},[660,661,662,663],[576,2150,2152],{"className":2151},[626,663],[576,2153,2047],{"className":2154},[626,663],[576,2156,2157,2160],{"style":1115},[576,2158],{"className":2159,"style":1103},[655],[576,2161],{"className":2162,"style":1123},[1122],[576,2164,2165,2168],{"style":1126},[576,2166],{"className":2167,"style":1103},[655],[576,2169,2171],{"className":2170},[660,661,662,663],[576,2172,2174],{"className":2173},[626,663],[576,2175,851],{"className":2176},[626,663],[576,2178,671],{"className":2179},[670],[576,2181,2183],{"className":2182},[643],[576,2184,2186],{"className":2185,"style":1148},[647],[576,2187],{},[576,2189],{"className":2190},[1154,1083],".",[564,2193,999,2194,1002,2196,2616,2617,2797,2798,2838,2839,2970,2971,3011,3012,2191],{},[568,2195,553],{},[576,2197,2199,2250],{"className":2198},[579],[576,2200,2202],{"className":2201},[583],[585,2203,2204],{"xmlns":587},[589,2205,2206,2247],{},[592,2207,2208,2210,2212,2218,2220,2226,2228,2234,2236,2238,2240],{},[849,2209,851],{},[845,2211,1019],{},[1021,2213,2214,2216],{},[849,2215,851],{},[849,2217,1036],{},[845,2219,847],{},[1021,2221,2222,2224],{},[849,2223,851],{},[849,2225,2047],{},[845,2227,1019],{},[1021,2229,2230,2232],{},[849,2231,851],{},[849,2233,1565],{},[845,2235,847],{},[845,2237,1041],{},[845,2239,1279],{},[1021,2241,2242,2245],{},[598,2243,2244],{},"π",[849,2246,1530],{},[605,2248,2249],{"encoding":607},"1 - \\frac{1}{3} + \\frac{1}{5} - \\frac{1}{7} + \\ldots = \\frac{\\pi}{4}",[576,2251,2253,2271,2354,2437,2520,2539],{"className":2252,"ariaHidden":613},[612],[576,2254,2256,2259,2262,2265,2268],{"className":2255},[617],[576,2257],{"className":2258,"style":1054},[621],[576,2260,851],{"className":2261},[626],[576,2263],{"className":2264,"style":1062},[1061],[576,2266,1019],{"className":2267},[901],[576,2269],{"className":2270,"style":1062},[1061],[576,2272,2274,2277,2345,2348,2351],{"className":2273},[617],[576,2275],{"className":2276,"style":1075},[621],[576,2278,2280,2283,2342],{"className":2279},[626],[576,2281],{"className":2282},[1082,1083],[576,2284,2286],{"className":2285},[1021],[576,2287,2289,2334],{"className":2288},[638,639],[576,2290,2292,2331],{"className":2291},[643],[576,2293,2295,2309,2317],{"className":2294,"style":1096},[647],[576,2296,2297,2300],{"style":1099},[576,2298],{"className":2299,"style":1103},[655],[576,2301,2303],{"className":2302},[660,661,662,663],[576,2304,2306],{"className":2305},[626,663],[576,2307,1036],{"className":2308},[626,663],[576,2310,2311,2314],{"style":1115},[576,2312],{"className":2313,"style":1103},[655],[576,2315],{"className":2316,"style":1123},[1122],[576,2318,2319,2322],{"style":1126},[576,2320],{"className":2321,"style":1103},[655],[576,2323,2325],{"className":2324},[660,661,662,663],[576,2326,2328],{"className":2327},[626,663],[576,2329,851],{"className":2330},[626,663],[576,2332,671],{"className":2333},[670],[576,2335,2337],{"className":2336},[643],[576,2338,2340],{"className":2339,"style":1148},[647],[576,2341],{},[576,2343],{"className":2344},[1154,1083],[576,2346],{"className":2347,"style":1062},[1061],[576,2349,847],{"className":2350},[901],[576,2352],{"className":2353,"style":1062},[1061],[576,2355,2357,2360,2428,2431,2434],{"className":2356},[617],[576,2358],{"className":2359,"style":1075},[621],[576,2361,2363,2366,2425],{"className":2362},[626],[576,2364],{"className":2365},[1082,1083],[576,2367,2369],{"className":2368},[1021],[576,2370,2372,2417],{"className":2371},[638,639],[576,2373,2375,2414],{"className":2374},[643],[576,2376,2378,2392,2400],{"className":2377,"style":1096},[647],[576,2379,2380,2383],{"style":1099},[576,2381],{"className":2382,"style":1103},[655],[576,2384,2386],{"className":2385},[660,661,662,663],[576,2387,2389],{"className":2388},[626,663],[576,2390,2047],{"className":2391},[626,663],[576,2393,2394,2397],{"style":1115},[576,2395],{"className":2396,"style":1103},[655],[576,2398],{"className":2399,"style":1123},[1122],[576,2401,2402,2405],{"style":1126},[576,2403],{"className":2404,"style":1103},[655],[576,2406,2408],{"className":2407},[660,661,662,663],[576,2409,2411],{"className":2410},[626,663],[576,2412,851],{"className":2413},[626,663],[576,2415,671],{"className":2416},[670],[576,2418,2420],{"className":2419},[643],[576,2421,2423],{"className":2422,"style":1148},[647],[576,2424],{},[576,2426],{"className":2427},[1154,1083],[576,2429],{"className":2430,"style":1062},[1061],[576,2432,1019],{"className":2433},[901],[576,2435],{"className":2436,"style":1062},[1061],[576,2438,2440,2443,2511,2514,2517],{"className":2439},[617],[576,2441],{"className":2442,"style":1075},[621],[576,2444,2446,2449,2508],{"className":2445},[626],[576,2447],{"className":2448},[1082,1083],[576,2450,2452],{"className":2451},[1021],[576,2453,2455,2500],{"className":2454},[638,639],[576,2456,2458,2497],{"className":2457},[643],[576,2459,2461,2475,2483],{"className":2460,"style":1096},[647],[576,2462,2463,2466],{"style":1099},[576,2464],{"className":2465,"style":1103},[655],[576,2467,2469],{"className":2468},[660,661,662,663],[576,2470,2472],{"className":2471},[626,663],[576,2473,1565],{"className":2474},[626,663],[576,2476,2477,2480],{"style":1115},[576,2478],{"className":2479,"style":1103},[655],[576,2481],{"className":2482,"style":1123},[1122],[576,2484,2485,2488],{"style":1126},[576,2486],{"className":2487,"style":1103},[655],[576,2489,2491],{"className":2490},[660,661,662,663],[576,2492,2494],{"className":2493},[626,663],[576,2495,851],{"className":2496},[626,663],[576,2498,671],{"className":2499},[670],[576,2501,2503],{"className":2502},[643],[576,2504,2506],{"className":2505,"style":1148},[647],[576,2507],{},[576,2509],{"className":2510},[1154,1083],[576,2512],{"className":2513,"style":1062},[1061],[576,2515,847],{"className":2516},[901],[576,2518],{"className":2519,"style":1062},[1061],[576,2521,2523,2527,2530,2533,2536],{"className":2522},[617],[576,2524],{"className":2525,"style":2526},[621],"height:0.3669em;",[576,2528,1041],{"className":2529},[1257],[576,2531],{"className":2532,"style":1341},[1061],[576,2534,1279],{"className":2535},[1345],[576,2537],{"className":2538,"style":1341},[1061],[576,2540,2542,2546],{"className":2541},[617],[576,2543],{"className":2544,"style":2545},[621],"height:1.0404em;vertical-align:-0.345em;",[576,2547,2549,2552,2613],{"className":2548},[626],[576,2550],{"className":2551},[1082,1083],[576,2553,2555],{"className":2554},[1021],[576,2556,2558,2605],{"className":2557},[638,639],[576,2559,2561,2602],{"className":2560},[643],[576,2562,2565,2579,2587],{"className":2563,"style":2564},[647],"height:0.6954em;",[576,2566,2567,2570],{"style":1099},[576,2568],{"className":2569,"style":1103},[655],[576,2571,2573],{"className":2572},[660,661,662,663],[576,2574,2576],{"className":2575},[626,663],[576,2577,1530],{"className":2578},[626,663],[576,2580,2581,2584],{"style":1115},[576,2582],{"className":2583,"style":1103},[655],[576,2585],{"className":2586,"style":1123},[1122],[576,2588,2589,2592],{"style":1126},[576,2590],{"className":2591,"style":1103},[655],[576,2593,2595],{"className":2594},[660,661,662,663],[576,2596,2598],{"className":2597},[626,663],[576,2599,2244],{"className":2600,"style":2601},[626,630,663],"margin-right:0.0359em;",[576,2603,671],{"className":2604},[670],[576,2606,2608],{"className":2607},[643],[576,2609,2611],{"className":2610,"style":1148},[647],[576,2612],{},[576,2614],{"className":2615},[1154,1083]," hat ",[576,2618,2620,2654],{"className":2619},[579],[576,2621,2623],{"className":2622},[583],[585,2624,2625],{"xmlns":587},[589,2626,2627,2651],{},[592,2628,2629,2635,2637],{},[595,2630,2631,2633],{},[598,2632,600],{},[598,2634,603],{},[845,2636,1279],{},[1021,2638,2639,2641],{},[849,2640,851],{},[592,2642,2643,2645,2647,2649],{},[849,2644,1027],{},[598,2646,603],{},[845,2648,1019],{},[849,2650,851],{},[605,2652,2653],{"encoding":607},"a_n = \\frac{1}{2n - 1}",[576,2655,2657,2712],{"className":2656,"ariaHidden":613},[612],[576,2658,2660,2663,2703,2706,2709],{"className":2659},[617],[576,2661],{"className":2662,"style":622},[621],[576,2664,2666,2669],{"className":2665},[626],[576,2667,600],{"className":2668},[626,630],[576,2670,2672],{"className":2671},[634],[576,2673,2675,2695],{"className":2674},[638,639],[576,2676,2678,2692],{"className":2677},[643],[576,2679,2681],{"className":2680,"style":648},[647],[576,2682,2683,2686],{"style":651},[576,2684],{"className":2685,"style":656},[655],[576,2687,2689],{"className":2688},[660,661,662,663],[576,2690,603],{"className":2691},[626,630,663],[576,2693,671],{"className":2694},[670],[576,2696,2698],{"className":2697},[643],[576,2699,2701],{"className":2700,"style":678},[647],[576,2702],{},[576,2704],{"className":2705,"style":1341},[1061],[576,2707,1279],{"className":2708},[1345],[576,2710],{"className":2711,"style":1341},[1061],[576,2713,2715,2719],{"className":2714},[617],[576,2716],{"className":2717,"style":2718},[621],"height:1.2484em;vertical-align:-0.4033em;",[576,2720,2722,2725,2794],{"className":2721},[626],[576,2723],{"className":2724},[1082,1083],[576,2726,2728],{"className":2727},[1021],[576,2729,2731,2785],{"className":2730},[638,639],[576,2732,2734,2782],{"className":2733},[643],[576,2735,2737,2760,2768],{"className":2736,"style":1096},[647],[576,2738,2739,2742],{"style":1099},[576,2740],{"className":2741,"style":1103},[655],[576,2743,2745],{"className":2744},[660,661,662,663],[576,2746,2748,2751,2754,2757],{"className":2747},[626,663],[576,2749,1027],{"className":2750},[626,663],[576,2752,603],{"className":2753},[626,630,663],[576,2755,1019],{"className":2756},[901,663],[576,2758,851],{"className":2759},[626,663],[576,2761,2762,2765],{"style":1115},[576,2763],{"className":2764,"style":1103},[655],[576,2766],{"className":2767,"style":1123},[1122],[576,2769,2770,2773],{"style":1126},[576,2771],{"className":2772,"style":1103},[655],[576,2774,2776],{"className":2775},[660,661,662,663],[576,2777,2779],{"className":2778},[626,663],[576,2780,851],{"className":2781},[626,663],[576,2783,671],{"className":2784},[670],[576,2786,2788],{"className":2787},[643],[576,2789,2792],{"className":2790,"style":2791},[647],"height:0.4033em;",[576,2793],{},[576,2795],{"className":2796},[1154,1083],". Mit vier Gliedern ergibt sich ",[576,2799,2801,2816],{"className":2800},[579],[576,2802,2804],{"className":2803},[583],[585,2805,2806],{"xmlns":587},[589,2807,2808,2813],{},[592,2809,2810],{},[849,2811,2812],{},"0,7238",[605,2814,2815],{"encoding":607},"0{,}7238",[576,2817,2819],{"className":2818,"ariaHidden":613},[612],[576,2820,2822,2825,2828,2834],{"className":2821},[617],[576,2823],{"className":2824,"style":1489},[621],[576,2826,1493],{"className":2827},[626],[576,2829,2831],{"className":2830},[626],[576,2832,1501],{"className":2833},[1500],[576,2835,2837],{"className":2836},[626],"7238",", der genaue Wert ist ",[576,2840,2842,2865],{"className":2841},[579],[576,2843,2845],{"className":2844},[583],[585,2846,2847],{"xmlns":587},[589,2848,2849,2862],{},[592,2850,2851,2857,2859],{},[1021,2852,2853,2855],{},[598,2854,2244],{},[849,2856,1530],{},[845,2858,1446],{},[849,2860,2861],{},"0,7854",[605,2863,2864],{"encoding":607},"\\frac{\\pi}{4} \\approx 0{,}7854",[576,2866,2868,2951],{"className":2867,"ariaHidden":613},[612],[576,2869,2871,2874,2942,2945,2948],{"className":2870},[617],[576,2872],{"className":2873,"style":2545},[621],[576,2875,2877,2880,2939],{"className":2876},[626],[576,2878],{"className":2879},[1082,1083],[576,2881,2883],{"className":2882},[1021],[576,2884,2886,2931],{"className":2885},[638,639],[576,2887,2889,2928],{"className":2888},[643],[576,2890,2892,2906,2914],{"className":2891,"style":2564},[647],[576,2893,2894,2897],{"style":1099},[576,2895],{"className":2896,"style":1103},[655],[576,2898,2900],{"className":2899},[660,661,662,663],[576,2901,2903],{"className":2902},[626,663],[576,2904,1530],{"className":2905},[626,663],[576,2907,2908,2911],{"style":1115},[576,2909],{"className":2910,"style":1103},[655],[576,2912],{"className":2913,"style":1123},[1122],[576,2915,2916,2919],{"style":1126},[576,2917],{"className":2918,"style":1103},[655],[576,2920,2922],{"className":2921},[660,661,662,663],[576,2923,2925],{"className":2924},[626,663],[576,2926,2244],{"className":2927,"style":2601},[626,630,663],[576,2929,671],{"className":2930},[670],[576,2932,2934],{"className":2933},[643],[576,2935,2937],{"className":2936,"style":1148},[647],[576,2938],{},[576,2940],{"className":2941},[1154,1083],[576,2943],{"className":2944,"style":1341},[1061],[576,2946,1446],{"className":2947},[1345],[576,2949],{"className":2950,"style":1341},[1061],[576,2952,2954,2957,2960,2966],{"className":2953},[617],[576,2955],{"className":2956,"style":1489},[621],[576,2958,1493],{"className":2959},[626],[576,2961,2963],{"className":2962},[626],[576,2964,1501],{"className":2965},[1500],[576,2967,2969],{"className":2968},[626],"7854",". Der Fehler ",[576,2972,2974,2989],{"className":2973},[579],[576,2975,2977],{"className":2976},[583],[585,2978,2979],{"xmlns":587},[589,2980,2981,2986],{},[592,2982,2983],{},[849,2984,2985],{},"0,0616",[605,2987,2988],{"encoding":607},"0{,}0616",[576,2990,2992],{"className":2991,"ariaHidden":613},[612],[576,2993,2995,2998,3001,3007],{"className":2994},[617],[576,2996],{"className":2997,"style":1489},[621],[576,2999,1493],{"className":3000},[626],[576,3002,3004],{"className":3003},[626],[576,3005,1501],{"className":3006},[1500],[576,3008,3010],{"className":3009},[626],"0616"," liegt unter der Schranke ",[576,3013,3015,3039],{"className":3014},[579],[576,3016,3018],{"className":3017},[583],[585,3019,3020],{"xmlns":587},[589,3021,3022,3036],{},[592,3023,3024,3031,3033],{},[1021,3025,3026,3028],{},[849,3027,851],{},[849,3029,3030],{},"9",[845,3032,1446],{},[849,3034,3035],{},"0,111",[605,3037,3038],{"encoding":607},"\\frac{1}{9} \\approx 0{,}111",[576,3040,3042,3125],{"className":3041,"ariaHidden":613},[612],[576,3043,3045,3048,3116,3119,3122],{"className":3044},[617],[576,3046],{"className":3047,"style":1075},[621],[576,3049,3051,3054,3113],{"className":3050},[626],[576,3052],{"className":3053},[1082,1083],[576,3055,3057],{"className":3056},[1021],[576,3058,3060,3105],{"className":3059},[638,639],[576,3061,3063,3102],{"className":3062},[643],[576,3064,3066,3080,3088],{"className":3065,"style":1096},[647],[576,3067,3068,3071],{"style":1099},[576,3069],{"className":3070,"style":1103},[655],[576,3072,3074],{"className":3073},[660,661,662,663],[576,3075,3077],{"className":3076},[626,663],[576,3078,3030],{"className":3079},[626,663],[576,3081,3082,3085],{"style":1115},[576,3083],{"className":3084,"style":1103},[655],[576,3086],{"className":3087,"style":1123},[1122],[576,3089,3090,3093],{"style":1126},[576,3091],{"className":3092,"style":1103},[655],[576,3094,3096],{"className":3095},[660,661,662,663],[576,3097,3099],{"className":3098},[626,663],[576,3100,851],{"className":3101},[626,663],[576,3103,671],{"className":3104},[670],[576,3106,3108],{"className":3107},[643],[576,3109,3111],{"className":3110,"style":1148},[647],[576,3112],{},[576,3114],{"className":3115},[1154,1083],[576,3117],{"className":3118,"style":1341},[1061],[576,3120,1446],{"className":3121},[1345],[576,3123],{"className":3124,"style":1341},[1061],[576,3126,3128,3131,3134,3140],{"className":3127},[617],[576,3129],{"className":3130,"style":1489},[621],[576,3132,1493],{"className":3133},[626],[576,3135,3137],{"className":3136},[626],[576,3138,1501],{"className":3139},[1500],[576,3141,3143],{"className":3142},[626],"111",[564,3145,3146,3147,3223,3224,3478,3479,3534,3535,3586,3587,2191],{},"Wie viele Glieder der alternierenden harmonischen Reihe garantieren einen Fehler von höchstens ",[576,3148,3150,3174],{"className":3149},[579],[576,3151,3153],{"className":3152},[583],[585,3154,3155],{"xmlns":587},[589,3156,3157,3171],{},[592,3158,3159],{},[3160,3161,3162,3165],"msup",{},[849,3163,3164],{},"10",[592,3166,3167,3169],{},[845,3168,1019],{},[849,3170,1036],{},[605,3172,3173],{"encoding":607},"10^{-3}",[576,3175,3177],{"className":3176,"ariaHidden":613},[612],[576,3178,3180,3184,3187],{"className":3179},[617],[576,3181],{"className":3182,"style":3183},[621],"height:0.8141em;",[576,3185,851],{"className":3186},[626],[576,3188,3190,3193],{"className":3189},[626],[576,3191,1493],{"className":3192},[626],[576,3194,3196],{"className":3195},[634],[576,3197,3199],{"className":3198},[638],[576,3200,3202],{"className":3201},[643],[576,3203,3205],{"className":3204,"style":3183},[647],[576,3206,3208,3211],{"style":3207},"top:-3.063em;margin-right:0.05em;",[576,3209],{"className":3210,"style":656},[655],[576,3212,3214],{"className":3213},[660,661,662,663],[576,3215,3217,3220],{"className":3216},[626,663],[576,3218,1019],{"className":3219},[626,663],[576,3221,1036],{"className":3222},[626,663],"? Aus ",[576,3225,3227,3278],{"className":3226},[579],[576,3228,3230],{"className":3229},[583],[585,3231,3232],{"xmlns":587},[589,3233,3234,3275],{},[592,3235,3236,3248,3250,3262,3265],{},[595,3237,3238,3240],{},[598,3239,600],{},[592,3241,3242,3244,3246],{},[598,3243,603],{},[845,3245,847],{},[849,3247,851],{},[845,3249,1279],{},[1021,3251,3252,3254],{},[849,3253,851],{},[592,3255,3256,3258,3260],{},[598,3257,603],{},[845,3259,847],{},[849,3261,851],{},[845,3263,3264],{},"≤",[3160,3266,3267,3269],{},[849,3268,3164],{},[592,3270,3271,3273],{},[845,3272,1019],{},[849,3274,1036],{},[605,3276,3277],{"encoding":607},"a_{n+1} = \\frac{1}{n + 1} \\leq 10^{-3}",[576,3279,3281,3345,3434],{"className":3280,"ariaHidden":613},[612],[576,3282,3284,3287,3336,3339,3342],{"className":3283},[617],[576,3285],{"className":3286,"style":864},[621],[576,3288,3290,3293],{"className":3289},[626],[576,3291,600],{"className":3292},[626,630],[576,3294,3296],{"className":3295},[634],[576,3297,3299,3328],{"className":3298},[638,639],[576,3300,3302,3325],{"className":3301},[643],[576,3303,3305],{"className":3304,"style":883},[647],[576,3306,3307,3310],{"style":651},[576,3308],{"className":3309,"style":656},[655],[576,3311,3313],{"className":3312},[660,661,662,663],[576,3314,3316,3319,3322],{"className":3315},[626,663],[576,3317,603],{"className":3318},[626,630,663],[576,3320,847],{"className":3321},[901,663],[576,3323,851],{"className":3324},[626,663],[576,3326,671],{"className":3327},[670],[576,3329,3331],{"className":3330},[643],[576,3332,3334],{"className":3333,"style":914},[647],[576,3335],{},[576,3337],{"className":3338,"style":1341},[1061],[576,3340,1279],{"className":3341},[1345],[576,3343],{"className":3344,"style":1341},[1061],[576,3346,3348,3351,3425,3428,3431],{"className":3347},[617],[576,3349],{"className":3350,"style":2718},[621],[576,3352,3354,3357,3422],{"className":3353},[626],[576,3355],{"className":3356},[1082,1083],[576,3358,3360],{"className":3359},[1021],[576,3361,3363,3414],{"className":3362},[638,639],[576,3364,3366,3411],{"className":3365},[643],[576,3367,3369,3389,3397],{"className":3368,"style":1096},[647],[576,3370,3371,3374],{"style":1099},[576,3372],{"className":3373,"style":1103},[655],[576,3375,3377],{"className":3376},[660,661,662,663],[576,3378,3380,3383,3386],{"className":3379},[626,663],[576,3381,603],{"className":3382},[626,630,663],[576,3384,847],{"className":3385},[901,663],[576,3387,851],{"className":3388},[626,663],[576,3390,3391,3394],{"style":1115},[576,3392],{"className":3393,"style":1103},[655],[576,3395],{"className":3396,"style":1123},[1122],[576,3398,3399,3402],{"style":1126},[576,3400],{"className":3401,"style":1103},[655],[576,3403,3405],{"className":3404},[660,661,662,663],[576,3406,3408],{"className":3407},[626,663],[576,3409,851],{"className":3410},[626,663],[576,3412,671],{"className":3413},[670],[576,3415,3417],{"className":3416},[643],[576,3418,3420],{"className":3419,"style":2791},[647],[576,3421],{},[576,3423],{"className":3424},[1154,1083],[576,3426],{"className":3427,"style":1341},[1061],[576,3429,3264],{"className":3430},[1345],[576,3432],{"className":3433,"style":1341},[1061],[576,3435,3437,3440,3443],{"className":3436},[617],[576,3438],{"className":3439,"style":3183},[621],[576,3441,851],{"className":3442},[626],[576,3444,3446,3449],{"className":3445},[626],[576,3447,1493],{"className":3448},[626],[576,3450,3452],{"className":3451},[634],[576,3453,3455],{"className":3454},[638],[576,3456,3458],{"className":3457},[643],[576,3459,3461],{"className":3460,"style":3183},[647],[576,3462,3463,3466],{"style":3207},[576,3464],{"className":3465,"style":656},[655],[576,3467,3469],{"className":3468},[660,661,662,663],[576,3470,3472,3475],{"className":3471},[626,663],[576,3473,1019],{"className":3474},[626,663],[576,3476,1036],{"className":3477},[626,663]," folgt ",[576,3480,3482,3502],{"className":3481},[579],[576,3483,3485],{"className":3484},[583],[585,3486,3487],{"xmlns":587},[589,3488,3489,3499],{},[592,3490,3491,3493,3496],{},[598,3492,603],{},[845,3494,3495],{},"≥",[849,3497,3498],{},"999",[605,3500,3501],{"encoding":607},"n \\geq 999",[576,3503,3505,3524],{"className":3504,"ariaHidden":613},[612],[576,3506,3508,3512,3515,3518,3521],{"className":3507},[617],[576,3509],{"className":3510,"style":3511},[621],"height:0.7719em;vertical-align:-0.136em;",[576,3513,603],{"className":3514},[626,630],[576,3516],{"className":3517,"style":1341},[1061],[576,3519,3495],{"className":3520},[1345],[576,3522],{"className":3523,"style":1341},[1061],[576,3525,3527,3531],{"className":3526},[617],[576,3528],{"className":3529,"style":3530},[621],"height:0.6444em;",[576,3532,3498],{"className":3533},[626],". Tatsächlich ist der Fehler bei ",[576,3536,3538,3556],{"className":3537},[579],[576,3539,3541],{"className":3540},[583],[585,3542,3543],{"xmlns":587},[589,3544,3545,3553],{},[592,3546,3547,3549,3551],{},[598,3548,603],{},[845,3550,1279],{},[849,3552,3498],{},[605,3554,3555],{"encoding":607},"n = 999",[576,3557,3559,3577],{"className":3558,"ariaHidden":613},[612],[576,3560,3562,3565,3568,3571,3574],{"className":3561},[617],[576,3563],{"className":3564,"style":715},[621],[576,3566,603],{"className":3567},[626,630],[576,3569],{"className":3570,"style":1341},[1061],[576,3572,1279],{"className":3573},[1345],[576,3575],{"className":3576,"style":1341},[1061],[576,3578,3580,3583],{"className":3579},[617],[576,3581],{"className":3582,"style":3530},[621],[576,3584,3498],{"className":3585},[626]," etwa ",[576,3588,3590,3605],{"className":3589},[579],[576,3591,3593],{"className":3592},[583],[585,3594,3595],{"xmlns":587},[589,3596,3597,3602],{},[592,3598,3599],{},[849,3600,3601],{},"0,0005",[605,3603,3604],{"encoding":607},"0{,}0005",[576,3606,3608],{"className":3607,"ariaHidden":613},[612],[576,3609,3611,3614,3617,3623],{"className":3610},[617],[576,3612],{"className":3613,"style":1489},[621],[576,3615,1493],{"className":3616},[626],[576,3618,3620],{"className":3619},[626],[576,3621,1501],{"className":3622},[1500],[576,3624,3626],{"className":3625},[626],"0005",[559,3628,3630],{"id":3629},"typische-fehler","Typische Fehler",[3632,3633,3634,3638,3641,3806],"ul",{},[3635,3636,3637],"li",{},"Die Monotonie nicht prüfen. Eine alternierende Reihe mit Nullfolge, aber nicht monotonen Beträgen kann divergieren.",[3635,3639,3640],{},"Aus dem Leibniz-Kriterium absolute Konvergenz folgern.",[3635,3642,3643,3644,3647,3648,3717,3718,3647,3721,3805],{},"Die Fehlerschranke mit dem letzten ",[568,3645,3646],{},"addierten"," Glied ",[576,3649,3651,3668],{"className":3650},[579],[576,3652,3654],{"className":3653},[583],[585,3655,3656],{"xmlns":587},[589,3657,3658,3666],{},[592,3659,3660],{},[595,3661,3662,3664],{},[598,3663,600],{},[598,3665,603],{},[605,3667,608],{"encoding":607},[576,3669,3671],{"className":3670,"ariaHidden":613},[612],[576,3672,3674,3677],{"className":3673},[617],[576,3675],{"className":3676,"style":622},[621],[576,3678,3680,3683],{"className":3679},[626],[576,3681,600],{"className":3682},[626,630],[576,3684,3686],{"className":3685},[634],[576,3687,3689,3709],{"className":3688},[638,639],[576,3690,3692,3706],{"className":3691},[643],[576,3693,3695],{"className":3694,"style":648},[647],[576,3696,3697,3700],{"style":651},[576,3698],{"className":3699,"style":656},[655],[576,3701,3703],{"className":3702},[660,661,662,663],[576,3704,603],{"className":3705},[626,630,663],[576,3707,671],{"className":3708},[670],[576,3710,3712],{"className":3711},[643],[576,3713,3715],{"className":3714,"style":678},[647],[576,3716],{}," statt mit dem ersten ",[568,3719,3720],{},"weggelassenen",[576,3722,3724,3747],{"className":3723},[579],[576,3725,3727],{"className":3726},[583],[585,3728,3729],{"xmlns":587},[589,3730,3731,3745],{},[592,3732,3733],{},[595,3734,3735,3737],{},[598,3736,600],{},[592,3738,3739,3741,3743],{},[598,3740,603],{},[845,3742,847],{},[849,3744,851],{},[605,3746,854],{"encoding":607},[576,3748,3750],{"className":3749,"ariaHidden":613},[612],[576,3751,3753,3756],{"className":3752},[617],[576,3754],{"className":3755,"style":864},[621],[576,3757,3759,3762],{"className":3758},[626],[576,3760,600],{"className":3761},[626,630],[576,3763,3765],{"className":3764},[634],[576,3766,3768,3797],{"className":3767},[638,639],[576,3769,3771,3794],{"className":3770},[643],[576,3772,3774],{"className":3773,"style":883},[647],[576,3775,3776,3779],{"style":651},[576,3777],{"className":3778,"style":656},[655],[576,3780,3782],{"className":3781},[660,661,662,663],[576,3783,3785,3788,3791],{"className":3784},[626,663],[576,3786,603],{"className":3787},[626,630,663],[576,3789,847],{"className":3790},[901,663],[576,3792,851],{"className":3793},[626,663],[576,3795,671],{"className":3796},[670],[576,3798,3800],{"className":3799},[643],[576,3801,3803],{"className":3802,"style":914},[647],[576,3804],{}," bilden.",[3635,3807,3808],{},"Das Kriterium auf Reihen anwenden, deren Vorzeichen nicht streng abwechseln.",{"title":3810,"searchDepth":3811,"depth":3811,"links":3812},"",2,[3813,3814,3815],{"id":561,"depth":3811,"text":562},{"id":995,"depth":3811,"text":996},{"id":3629,"depth":3811,"text":3630},[3817,3820,3822,3825,3828,3831,3834,3837,3840,3843,3845],{"lhs":3818,"rhs":3819},"1 - 1\u002F2 + 1\u002F3 - 1\u002F4","7\u002F12",{"lhs":3821,"rhs":3819},"sum((-1).^(0:3) .\u002F (1:4))",{"lhs":3823,"rhs":3824},"round(7\u002F12, 4)","0.5833",{"lhs":3826,"rhs":3827},"round(log(2), 4)","0.6931",{"lhs":3829,"rhs":3830},"round(abs(log(2) - 7\u002F12), 4)","0.1098",{"lhs":3832,"rhs":3833},"round(sum((-1).^(0:3) .\u002F (2*(0:3) + 1)), 4)","0.7238",{"lhs":3835,"rhs":3836},"round(pi\u002F4, 4)","0.7854",{"lhs":3838,"rhs":3839},"round(pi\u002F4 - sum((-1).^(0:3) .\u002F (2*(0:3) + 1)), 4)","0.0616",{"lhs":3841,"rhs":3842},"round(1\u002F9, 3)","0.111",{"lhs":3844,"rhs":3498},"10^3 - 1",{"lhs":3846,"rhs":3847},"round(abs(log(2) - sum((-1).^(0:998) .\u002F (1:999))), 4)","0.0005","(a_n) \\text{ monoton fallend},\\ \\lim_{n \\to \\infty} a_n = 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">(a_n)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">monoton\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">fallend\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.3em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmrow>\u003Cmi>lim\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>→\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\lim_{n \\to \\infty} a_n = 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8444em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mop\">lim\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">→\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","leibniz-criterion","\\sum_{n=1}^{\\infty} (-1)^{n+1} a_n \\text{ konvergiert}, \\quad |s - s_n| \\leq a_{n+1}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmunderover>\u003Cmo>∑\u003C\u002Fmo>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmunderover>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmtext> konvergiert\u003C\u002Fmtext>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"1em\"\u002F>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmi>s\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>s\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\sum_{n=1}^{\\infty} (-1)^{n+1} a_n \\text{ konvergiert}, \\quad |s - s_n| \\leq a_{n+1}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.9185em;vertical-align:-1.2671em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.6514em;\">\u003Cspan style=\"top:-1.8829em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">=\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.05em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop op-symbol large-op\">∑\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-4.3em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.2671em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">−\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">+\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\"> konvergiert\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:1em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">s\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">s\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≤\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6389em;vertical-align:-0.2083em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">+\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.2083em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fleibniz-kriterium",[],[3861,3862,3863],"harmonic-series","ratio-test","root-test",{"title":548,"description":3810},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fleibniz-kriterium","Eine alternierende Reihe, deren Gliedbeträge monoton gegen 0 fallen, konvergiert; der Fehler ist höchstens das nächste Glied.",[3868,3869,3870,3871],"konvergenzkriterium","alternierende reihe","konvergenz","fehlerabschätzung",[3873,3876,3880,3883,3886],{"symbol":608,"meaning":3874,"symbolHtml":3875},"Betrag des n-ten Glieds, nicht negativ","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a_n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3877,"meaning":3878,"symbolHtml":3879},"(-1)^{n+1}","Vorzeichenwechsel, beginnend mit plus","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">(-1)^{n+1}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.0641em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">−\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">+\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":703,"meaning":3881,"symbolHtml":3882},"Wert (Grenzwert) der Reihe","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>s\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">s\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">s\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":773,"meaning":3884,"symbolHtml":3885},"n-te Partialsumme","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>s\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">s_n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">s\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":603,"meaning":3887,"symbolHtml":3888},"Index der Glieder","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","bkywZD1ZAp135CVP6xyhnlk0Hw1nTGxwushC5pl3Qjk",[3891,3894,3897],{"stem":3892,"title":3893,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fharmonische-reihe","Harmonische Reihe",{"stem":3895,"title":3896,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fquotientenkriterium","Quotientenkriterium",{"stem":3898,"title":3899,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fwurzelkriterium","Wurzelkriterium",1793824264392]