[{"data":1,"prerenderedAt":4412},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fintegralkriterium":546,"formula-related-de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fintegralkriterium":4399},[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":554,"category":412,"checks":4337,"conditions":4363,"conditionsHtml":4364,"deprecated":4365,"description":4331,"extension":4366,"figure":4365,"figureCaption":4365,"figureHtml":4365,"formulaId":4367,"latex":4368,"latexHtml":4369,"level":4370,"meta":4371,"navigation":4372,"path":4373,"redirectFrom":4374,"related":4375,"seo":4380,"stem":4381,"subject":580,"summary":4382,"tags":4383,"variables":4388,"__hash__":4398},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fintegralkriterium.md","Integralkriterium",[550,551,552,553],"Integralkriterium Reihe","Integralvergleichskriterium","Reihe mit Integral abschätzen","Cauchy-Integralkriterium",{"type":555,"value":556,"toc":4330},"minimark",[557,562,703,1189,1192,1199,1622,1625,1629,2050,2448,2923,3722,3726],[558,559,561],"h2",{"id":560},"erklärung","Erklärung",[563,564,565,566,569,570,617,618,670,671,702],"p",{},"Das ",[567,568,548],"strong",{}," übersetzt eine Reihenfrage in eine Integralfrage. Weil ",[571,572,575,597],"span",{"className":573},[574],"katex",[571,576,579],{"className":577},[578],"katex-mathml",[580,581,583],"math",{"xmlns":582},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[584,585,586,593],"semantics",{},[587,588,589],"mrow",{},[590,591,592],"mi",{},"f",[594,595,592],"annotation",{"encoding":596},"application\u002Fx-tex",[571,598,602],{"className":599,"ariaHidden":601},[600],"katex-html","true",[571,603,606,611],{"className":604},[605],"base",[571,607],{"className":608,"style":610},[609],"strut","height:0.8889em;vertical-align:-0.1944em;",[571,612,592],{"className":613,"style":616},[614,615],"mord","mathnormal","margin-right:0.1076em;"," monoton fällt, liegen die Rechtecke mit Höhe ",[571,619,621,646],{"className":620},[574],[571,622,624],{"className":623},[578],[580,625,626],{"xmlns":582},[584,627,628,643],{},[587,629,630,632,637,640],{},[590,631,592],{},[633,634,636],"mo",{"stretchy":635},"false","(",[590,638,639],{},"n",[633,641,642],{"stretchy":635},")",[594,644,645],{"encoding":596},"f(n)",[571,647,649],{"className":648,"ariaHidden":601},[600],[571,650,652,656,659,663,666],{"className":651},[605],[571,653],{"className":654,"style":655},[609],"height:1em;vertical-align:-0.25em;",[571,657,592],{"className":658,"style":616},[614,615],[571,660,636],{"className":661},[662],"mopen",[571,664,639],{"className":665},[614,615],[571,667,642],{"className":668},[669],"mclose"," und Breite ",[571,672,674,689],{"className":673},[574],[571,675,677],{"className":676},[578],[580,678,679],{"xmlns":582},[584,680,681,687],{},[587,682,683],{},[684,685,686],"mn",{},"1",[594,688,686],{"encoding":596},[571,690,692],{"className":691,"ariaHidden":601},[600],[571,693,695,699],{"className":694},[605],[571,696],{"className":697,"style":698},[609],"height:0.6444em;",[571,700,686],{"className":701},[614]," einmal oberhalb und einmal unterhalb der Fläche unter dem Graphen. Daraus folgt die Abschätzung",[571,704,707],{"className":705},[706],"katex-display",[571,708,710,830],{"className":709},[574],[571,711,713],{"className":712},[578],[580,714,716],{"xmlns":582,"display":715},"block",[584,717,718,827],{},[587,719,720,738,740,742,745,747,751,754,756,759,762,764,781,783,785,787,789,791,793,795,797,799,801,803,805,813,815,817,819,821,823,825],{},[721,722,723,726,728],"msubsup",{},[633,724,725],{},"∫",[684,727,686],{},[587,729,730,733,736],{},[590,731,732],{},"N",[633,734,735],{},"+",[684,737,686],{},[590,739,592],{},[633,741,636],{"stretchy":635},[590,743,744],{},"x",[633,746,642],{"stretchy":635},[748,749,750],"mtext",{}," ",[590,752,753],{},"d",[590,755,744],{},[748,757,758],{},"  ",[633,760,761],{},"≤",[748,763,758],{},[765,766,767,770,779],"munderover",{},[633,768,769],{},"∑",[587,771,772,774,777],{},[590,773,639],{},[633,775,776],{},"=",[684,778,686],{},[590,780,732],{},[590,782,592],{},[633,784,636],{"stretchy":635},[590,786,639],{},[633,788,642],{"stretchy":635},[748,790,758],{},[633,792,761],{},[748,794,758],{},[590,796,592],{},[633,798,636],{"stretchy":635},[684,800,686],{},[633,802,642],{"stretchy":635},[633,804,735],{},[721,806,807,809,811],{},[633,808,725],{},[684,810,686],{},[590,812,732],{},[590,814,592],{},[633,816,636],{"stretchy":635},[590,818,744],{},[633,820,642],{"stretchy":635},[748,822,750],{},[590,824,753],{},[590,826,744],{},[594,828,829],{"encoding":596},"\\int_1^{N+1} f(x)\\,dx \\;\\leq\\; \\sum_{n=1}^{N} f(n) \\;\\leq\\; f(1) + \\int_1^{N} f(x)\\,dx",[571,831,833,966,1077,1105],{"className":832,"ariaHidden":601},[600],[571,834,836,840,923,928,931,934,937,940,943,946,949,953,956,960,963],{"className":835},[605],[571,837],{"className":838,"style":839},[609],"height:2.5032em;vertical-align:-0.9119em;",[571,841,844,850],{"className":842},[843],"mop",[571,845,725],{"className":846,"style":849},[843,847,848],"op-symbol","large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[571,851,854],{"className":852},[853],"msupsub",[571,855,859,914],{"className":856},[857,858],"vlist-t","vlist-t2",[571,860,863,909],{"className":861},[862],"vlist-r",[571,864,868,886],{"className":865,"style":867},[866],"vlist","height:1.5912em;",[571,869,871,876],{"style":870},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[571,872],{"className":873,"style":875},[874],"pstrut","height:2.7em;",[571,877,883],{"className":878},[879,880,881,882],"sizing","reset-size6","size3","mtight",[571,884,686],{"className":885},[614,882],[571,887,889,892],{"style":888},"top:-3.8129em;margin-right:0.05em;",[571,890],{"className":891,"style":875},[874],[571,893,895],{"className":894},[879,880,881,882],[571,896,898,902,906],{"className":897},[614,882],[571,899,732],{"className":900,"style":901},[614,615,882],"margin-right:0.109em;",[571,903,735],{"className":904},[905,882],"mbin",[571,907,686],{"className":908},[614,882],[571,910,913],{"className":911},[912],"vlist-s","​",[571,915,917],{"className":916},[862],[571,918,921],{"className":919,"style":920},[866],"height:0.9119em;",[571,922],{},[571,924],{"className":925,"style":927},[926],"mspace","margin-right:0.1667em;",[571,929,592],{"className":930,"style":616},[614,615],[571,932,636],{"className":933},[662],[571,935,744],{"className":936},[614,615],[571,938,642],{"className":939},[669],[571,941],{"className":942,"style":927},[926],[571,944,753],{"className":945},[614,615],[571,947,744],{"className":948},[614,615],[571,950],{"className":951,"style":952},[926],"margin-right:0.2778em;",[571,954],{"className":955,"style":952},[926],[571,957,761],{"className":958},[959],"mrel",[571,961],{"className":962,"style":952},[926],[571,964],{"className":965,"style":952},[926],[571,967,969,973,1047,1050,1053,1056,1059,1062,1065,1068,1071,1074],{"className":968},[605],[571,970],{"className":971,"style":972},[609],"height:3.0954em;vertical-align:-1.2671em;",[571,974,977],{"className":975},[843,976],"op-limits",[571,978,980,1038],{"className":979},[857,858],[571,981,983,1035],{"className":982},[862],[571,984,987,1009,1020],{"className":985,"style":986},[866],"height:1.8283em;",[571,988,990,994],{"style":989},"top:-1.8829em;margin-left:0em;",[571,991],{"className":992,"style":993},[874],"height:3.05em;",[571,995,997],{"className":996},[879,880,881,882],[571,998,1000,1003,1006],{"className":999},[614,882],[571,1001,639],{"className":1002},[614,615,882],[571,1004,776],{"className":1005},[959,882],[571,1007,686],{"className":1008},[614,882],[571,1010,1012,1015],{"style":1011},"top:-3.05em;",[571,1013],{"className":1014,"style":993},[874],[571,1016,1017],{},[571,1018,769],{"className":1019},[843,847,848],[571,1021,1023,1026],{"style":1022},"top:-4.3em;margin-left:0em;",[571,1024],{"className":1025,"style":993},[874],[571,1027,1029],{"className":1028},[879,880,881,882],[571,1030,1032],{"className":1031},[614,882],[571,1033,732],{"className":1034,"style":901},[614,615,882],[571,1036,913],{"className":1037},[912],[571,1039,1041],{"className":1040},[862],[571,1042,1045],{"className":1043,"style":1044},[866],"height:1.2671em;",[571,1046],{},[571,1048],{"className":1049,"style":927},[926],[571,1051,592],{"className":1052,"style":616},[614,615],[571,1054,636],{"className":1055},[662],[571,1057,639],{"className":1058},[614,615],[571,1060,642],{"className":1061},[669],[571,1063],{"className":1064,"style":952},[926],[571,1066],{"className":1067,"style":952},[926],[571,1069,761],{"className":1070},[959],[571,1072],{"className":1073,"style":952},[926],[571,1075],{"className":1076,"style":952},[926],[571,1078,1080,1083,1086,1089,1092,1095,1099,1102],{"className":1079},[605],[571,1081],{"className":1082,"style":655},[609],[571,1084,592],{"className":1085,"style":616},[614,615],[571,1087,636],{"className":1088},[662],[571,1090,686],{"className":1091},[614],[571,1093,642],{"className":1094},[669],[571,1096],{"className":1097,"style":1098},[926],"margin-right:0.2222em;",[571,1100,735],{"className":1101},[905],[571,1103],{"className":1104,"style":1098},[926],[571,1106,1108,1111,1165,1168,1171,1174,1177,1180,1183,1186],{"className":1107},[605],[571,1109],{"className":1110,"style":839},[609],[571,1112,1114,1117],{"className":1113},[843],[571,1115,725],{"className":1116,"style":849},[843,847,848],[571,1118,1120],{"className":1119},[853],[571,1121,1123,1157],{"className":1122},[857,858],[571,1124,1126,1154],{"className":1125},[862],[571,1127,1129,1140],{"className":1128,"style":867},[866],[571,1130,1131,1134],{"style":870},[571,1132],{"className":1133,"style":875},[874],[571,1135,1137],{"className":1136},[879,880,881,882],[571,1138,686],{"className":1139},[614,882],[571,1141,1142,1145],{"style":888},[571,1143],{"className":1144,"style":875},[874],[571,1146,1148],{"className":1147},[879,880,881,882],[571,1149,1151],{"className":1150},[614,882],[571,1152,732],{"className":1153,"style":901},[614,615,882],[571,1155,913],{"className":1156},[912],[571,1158,1160],{"className":1159},[862],[571,1161,1163],{"className":1162,"style":920},[866],[571,1164],{},[571,1166],{"className":1167,"style":927},[926],[571,1169,592],{"className":1170,"style":616},[614,615],[571,1172,636],{"className":1173},[662],[571,1175,744],{"className":1176},[614,615],[571,1178,642],{"className":1179},[669],[571,1181],{"className":1182,"style":927},[926],[571,1184,753],{"className":1185},[614,615],[571,1187,744],{"className":1188},[614,615],[563,1190,1191],{},"Bleiben die Integrale beschränkt, sind es auch die Teilsummen, und die Reihe konvergiert. Wachsen sie über alle Grenzen, divergiert die Reihe.",[563,1193,1194,1195,1198],{},"Für den ",[567,1196,1197],{},"Rest"," einer konvergenten Reihe gilt entsprechend",[571,1200,1202],{"className":1201},[706],[571,1203,1205,1307],{"className":1204},[574],[571,1206,1208],{"className":1207},[578],[580,1209,1210],{"xmlns":582,"display":715},[584,1211,1212,1304],{},[587,1213,1214,1230,1232,1234,1236,1238,1240,1242,1244,1246,1248,1250,1268,1270,1272,1274,1276,1278,1280,1282,1290,1292,1294,1296,1298,1300,1302],{},[721,1215,1216,1218,1226],{},[633,1217,725],{},[587,1219,1220,1222,1224],{},[590,1221,732],{},[633,1223,735],{},[684,1225,686],{},[590,1227,1229],{"mathvariant":1228},"normal","∞",[590,1231,592],{},[633,1233,636],{"stretchy":635},[590,1235,744],{},[633,1237,642],{"stretchy":635},[748,1239,750],{},[590,1241,753],{},[590,1243,744],{},[748,1245,758],{},[633,1247,761],{},[748,1249,758],{},[765,1251,1252,1254,1266],{},[633,1253,769],{},[587,1255,1256,1258,1260,1262,1264],{},[590,1257,639],{},[633,1259,776],{},[590,1261,732],{},[633,1263,735],{},[684,1265,686],{},[590,1267,1229],{"mathvariant":1228},[590,1269,592],{},[633,1271,636],{"stretchy":635},[590,1273,639],{},[633,1275,642],{"stretchy":635},[748,1277,758],{},[633,1279,761],{},[748,1281,758],{},[721,1283,1284,1286,1288],{},[633,1285,725],{},[590,1287,732],{},[590,1289,1229],{"mathvariant":1228},[590,1291,592],{},[633,1293,636],{"stretchy":635},[590,1295,744],{},[633,1297,642],{"stretchy":635},[748,1299,750],{},[590,1301,753],{},[590,1303,744],{},[594,1305,1306],{"encoding":596},"\\int_{N+1}^{\\infty} f(x)\\,dx \\;\\leq\\; \\sum_{n=N+1}^{\\infty} f(n) \\;\\leq\\; \\int_{N}^{\\infty} f(x)\\,dx",[571,1308,1310,1421,1534],{"className":1309,"ariaHidden":601},[600],[571,1311,1313,1317,1382,1385,1388,1391,1394,1397,1400,1403,1406,1409,1412,1415,1418],{"className":1312},[605],[571,1314],{"className":1315,"style":1316},[609],"height:2.3846em;vertical-align:-0.9703em;",[571,1318,1320,1323],{"className":1319},[843],[571,1321,725],{"className":1322,"style":849},[843,847,848],[571,1324,1326],{"className":1325},[853],[571,1327,1329,1373],{"className":1328},[857,858],[571,1330,1332,1370],{"className":1331},[862],[571,1333,1336,1356],{"className":1334,"style":1335},[866],"height:1.4143em;",[571,1337,1338,1341],{"style":870},[571,1339],{"className":1340,"style":875},[874],[571,1342,1344],{"className":1343},[879,880,881,882],[571,1345,1347,1350,1353],{"className":1346},[614,882],[571,1348,732],{"className":1349,"style":901},[614,615,882],[571,1351,735],{"className":1352},[905,882],[571,1354,686],{"className":1355},[614,882],[571,1357,1358,1361],{"style":888},[571,1359],{"className":1360,"style":875},[874],[571,1362,1364],{"className":1363},[879,880,881,882],[571,1365,1367],{"className":1366},[614,882],[571,1368,1229],{"className":1369},[614,882],[571,1371,913],{"className":1372},[912],[571,1374,1376],{"className":1375},[862],[571,1377,1380],{"className":1378,"style":1379},[866],"height:0.9703em;",[571,1381],{},[571,1383],{"className":1384,"style":927},[926],[571,1386,592],{"className":1387,"style":616},[614,615],[571,1389,636],{"className":1390},[662],[571,1392,744],{"className":1393},[614,615],[571,1395,642],{"className":1396},[669],[571,1398],{"className":1399,"style":927},[926],[571,1401,753],{"className":1402},[614,615],[571,1404,744],{"className":1405},[614,615],[571,1407],{"className":1408,"style":952},[926],[571,1410],{"className":1411,"style":952},[926],[571,1413,761],{"className":1414},[959],[571,1416],{"className":1417,"style":952},[926],[571,1419],{"className":1420,"style":952},[926],[571,1422,1424,1428,1504,1507,1510,1513,1516,1519,1522,1525,1528,1531],{"className":1423},[605],[571,1425],{"className":1426,"style":1427},[609],"height:3.0041em;vertical-align:-1.3527em;",[571,1429,1431],{"className":1430},[843,976],[571,1432,1434,1495],{"className":1433},[857,858],[571,1435,1437,1492],{"className":1436},[862],[571,1438,1441,1468,1478],{"className":1439,"style":1440},[866],"height:1.6514em;",[571,1442,1444,1447],{"style":1443},"top:-1.8557em;margin-left:0em;",[571,1445],{"className":1446,"style":993},[874],[571,1448,1450],{"className":1449},[879,880,881,882],[571,1451,1453,1456,1459,1462,1465],{"className":1452},[614,882],[571,1454,639],{"className":1455},[614,615,882],[571,1457,776],{"className":1458},[959,882],[571,1460,732],{"className":1461,"style":901},[614,615,882],[571,1463,735],{"className":1464},[905,882],[571,1466,686],{"className":1467},[614,882],[571,1469,1470,1473],{"style":1011},[571,1471],{"className":1472,"style":993},[874],[571,1474,1475],{},[571,1476,769],{"className":1477},[843,847,848],[571,1479,1480,1483],{"style":1022},[571,1481],{"className":1482,"style":993},[874],[571,1484,1486],{"className":1485},[879,880,881,882],[571,1487,1489],{"className":1488},[614,882],[571,1490,1229],{"className":1491},[614,882],[571,1493,913],{"className":1494},[912],[571,1496,1498],{"className":1497},[862],[571,1499,1502],{"className":1500,"style":1501},[866],"height:1.3527em;",[571,1503],{},[571,1505],{"className":1506,"style":927},[926],[571,1508,592],{"className":1509,"style":616},[614,615],[571,1511,636],{"className":1512},[662],[571,1514,639],{"className":1515},[614,615],[571,1517,642],{"className":1518},[669],[571,1520],{"className":1521,"style":952},[926],[571,1523],{"className":1524,"style":952},[926],[571,1526,761],{"className":1527},[959],[571,1529],{"className":1530,"style":952},[926],[571,1532],{"className":1533,"style":952},[926],[571,1535,1537,1541,1598,1601,1604,1607,1610,1613,1616,1619],{"className":1536},[605],[571,1538],{"className":1539,"style":1540},[609],"height:2.3262em;vertical-align:-0.9119em;",[571,1542,1544,1547],{"className":1543},[843],[571,1545,725],{"className":1546,"style":849},[843,847,848],[571,1548,1550],{"className":1549},[853],[571,1551,1553,1590],{"className":1552},[857,858],[571,1554,1556,1587],{"className":1555},[862],[571,1557,1559,1573],{"className":1558,"style":1335},[866],[571,1560,1561,1564],{"style":870},[571,1562],{"className":1563,"style":875},[874],[571,1565,1567],{"className":1566},[879,880,881,882],[571,1568,1570],{"className":1569},[614,882],[571,1571,732],{"className":1572,"style":901},[614,615,882],[571,1574,1575,1578],{"style":888},[571,1576],{"className":1577,"style":875},[874],[571,1579,1581],{"className":1580},[879,880,881,882],[571,1582,1584],{"className":1583},[614,882],[571,1585,1229],{"className":1586},[614,882],[571,1588,913],{"className":1589},[912],[571,1591,1593],{"className":1592},[862],[571,1594,1596],{"className":1595,"style":920},[866],[571,1597],{},[571,1599],{"className":1600,"style":927},[926],[571,1602,592],{"className":1603,"style":616},[614,615],[571,1605,636],{"className":1606},[662],[571,1608,744],{"className":1609},[614,615],[571,1611,642],{"className":1612},[669],[571,1614],{"className":1615,"style":927},[926],[571,1617,753],{"className":1618},[614,615],[571,1620,744],{"className":1621},[614,615],[563,1623,1624],{},"Damit lässt sich abschätzen, wie viele Glieder man für eine gewünschte Genauigkeit braucht. Die Reihe darf auch bei einem anderen Index starten; dann beginnt das Integral dort.",[558,1626,1628],{"id":1627},"beispiele","Beispiele",[563,1630,1631,1634,1635,1886,1887,1995,1996,2049],{},[567,1632,1633],{},"Harmonische Reihe:"," ",[571,1636,1638,1686],{"className":1637},[574],[571,1639,1641],{"className":1640},[578],[580,1642,1643],{"xmlns":582},[584,1644,1645,1683],{},[587,1646,1647,1655,1662,1664,1666,1668,1670,1673,1676,1678,1681],{},[721,1648,1649,1651,1653],{},[633,1650,725],{},[684,1652,686],{},[590,1654,732],{},[1656,1657,1658,1660],"mfrac",{},[684,1659,686],{},[590,1661,744],{},[748,1663,750],{},[590,1665,753],{},[590,1667,744],{},[633,1669,776],{},[590,1671,1672],{},"ln",[633,1674,1675],{},"⁡",[590,1677,732],{},[633,1679,1680],{},"→",[590,1682,1229],{"mathvariant":1228},[594,1684,1685],{"encoding":596},"\\int_1^N \\frac{1}{x}\\,dx = \\ln N \\to \\infty",[571,1687,1689,1851,1876],{"className":1688,"ariaHidden":601},[600],[571,1690,1692,1696,1753,1756,1833,1836,1839,1842,1845,1848],{"className":1691},[605],[571,1693],{"className":1694,"style":1695},[609],"height:1.3921em;vertical-align:-0.3558em;",[571,1697,1699,1704],{"className":1698},[843],[571,1700,725],{"className":1701,"style":1703},[843,847,1702],"small-op","margin-right:0.1945em;position:relative;top:-0.0006em;",[571,1705,1707],{"className":1706},[853],[571,1708,1710,1744],{"className":1709},[857,858],[571,1711,1713,1741],{"className":1712},[862],[571,1714,1717,1729],{"className":1715,"style":1716},[866],"height:1.0362em;",[571,1718,1720,1723],{"style":1719},"top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;",[571,1721],{"className":1722,"style":875},[874],[571,1724,1726],{"className":1725},[879,880,881,882],[571,1727,686],{"className":1728},[614,882],[571,1730,1732,1735],{"style":1731},"top:-3.2579em;margin-right:0.05em;",[571,1733],{"className":1734,"style":875},[874],[571,1736,1738],{"className":1737},[879,880,881,882],[571,1739,732],{"className":1740,"style":901},[614,615,882],[571,1742,913],{"className":1743},[912],[571,1745,1747],{"className":1746},[862],[571,1748,1751],{"className":1749,"style":1750},[866],"height:0.3558em;",[571,1752],{},[571,1754],{"className":1755,"style":927},[926],[571,1757,1759,1763,1830],{"className":1758},[614],[571,1760],{"className":1761},[662,1762],"nulldelimiter",[571,1764,1766],{"className":1765},[1656],[571,1767,1769,1821],{"className":1768},[857,858],[571,1770,1772,1818],{"className":1771},[862],[571,1773,1776,1792,1803],{"className":1774,"style":1775},[866],"height:0.8451em;",[571,1777,1779,1783],{"style":1778},"top:-2.655em;",[571,1780],{"className":1781,"style":1782},[874],"height:3em;",[571,1784,1786],{"className":1785},[879,880,881,882],[571,1787,1789],{"className":1788},[614,882],[571,1790,744],{"className":1791},[614,615,882],[571,1793,1795,1798],{"style":1794},"top:-3.23em;",[571,1796],{"className":1797,"style":1782},[874],[571,1799],{"className":1800,"style":1802},[1801],"frac-line","border-bottom-width:0.04em;",[571,1804,1806,1809],{"style":1805},"top:-3.394em;",[571,1807],{"className":1808,"style":1782},[874],[571,1810,1812],{"className":1811},[879,880,881,882],[571,1813,1815],{"className":1814},[614,882],[571,1816,686],{"className":1817},[614,882],[571,1819,913],{"className":1820},[912],[571,1822,1824],{"className":1823},[862],[571,1825,1828],{"className":1826,"style":1827},[866],"height:0.345em;",[571,1829],{},[571,1831],{"className":1832},[669,1762],[571,1834],{"className":1835,"style":927},[926],[571,1837,753],{"className":1838},[614,615],[571,1840,744],{"className":1841},[614,615],[571,1843],{"className":1844,"style":952},[926],[571,1846,776],{"className":1847},[959],[571,1849],{"className":1850,"style":952},[926],[571,1852,1854,1858,1861,1864,1867,1870,1873],{"className":1853},[605],[571,1855],{"className":1856,"style":1857},[609],"height:0.6944em;",[571,1859,1672],{"className":1860},[843],[571,1862],{"className":1863,"style":927},[926],[571,1865,732],{"className":1866,"style":901},[614,615],[571,1868],{"className":1869,"style":952},[926],[571,1871,1680],{"className":1872},[959],[571,1874],{"className":1875,"style":952},[926],[571,1877,1879,1883],{"className":1878},[605],[571,1880],{"className":1881,"style":1882},[609],"height:0.4306em;",[571,1884,1229],{"className":1885},[614],", also divergiert ",[571,1888,1890,1910],{"className":1889},[574],[571,1891,1893],{"className":1892},[578],[580,1894,1895],{"xmlns":582},[584,1896,1897,1907],{},[587,1898,1899,1901],{},[633,1900,769],{},[1656,1902,1903,1905],{},[684,1904,686],{},[590,1906,639],{},[594,1908,1909],{"encoding":596},"\\sum \\frac{1}{n}",[571,1911,1913],{"className":1912,"ariaHidden":601},[600],[571,1914,1916,1920,1924,1927],{"className":1915},[605],[571,1917],{"className":1918,"style":1919},[609],"height:1.1901em;vertical-align:-0.345em;",[571,1921,769],{"className":1922,"style":1923},[843,847,1702],"position:relative;top:0em;",[571,1925],{"className":1926,"style":927},[926],[571,1928,1930,1933,1992],{"className":1929},[614],[571,1931],{"className":1932},[662,1762],[571,1934,1936],{"className":1935},[1656],[571,1937,1939,1984],{"className":1938},[857,858],[571,1940,1942,1981],{"className":1941},[862],[571,1943,1945,1959,1967],{"className":1944,"style":1775},[866],[571,1946,1947,1950],{"style":1778},[571,1948],{"className":1949,"style":1782},[874],[571,1951,1953],{"className":1952},[879,880,881,882],[571,1954,1956],{"className":1955},[614,882],[571,1957,639],{"className":1958},[614,615,882],[571,1960,1961,1964],{"style":1794},[571,1962],{"className":1963,"style":1782},[874],[571,1965],{"className":1966,"style":1802},[1801],[571,1968,1969,1972],{"style":1805},[571,1970],{"className":1971,"style":1782},[874],[571,1973,1975],{"className":1974},[879,880,881,882],[571,1976,1978],{"className":1977},[614,882],[571,1979,686],{"className":1980},[614,882],[571,1982,913],{"className":1983},[912],[571,1985,1987],{"className":1986},[862],[571,1988,1990],{"className":1989,"style":1827},[866],[571,1991],{},[571,1993],{"className":1994},[669,1762],". Die Abschätzung für ",[571,1997,1999,2018],{"className":1998},[574],[571,2000,2002],{"className":2001},[578],[580,2003,2004],{"xmlns":582},[584,2005,2006,2015],{},[587,2007,2008,2010,2012],{},[590,2009,732],{},[633,2011,776],{},[684,2013,2014],{},"100",[594,2016,2017],{"encoding":596},"N = 100",[571,2019,2021,2040],{"className":2020,"ariaHidden":601},[600],[571,2022,2024,2028,2031,2034,2037],{"className":2023},[605],[571,2025],{"className":2026,"style":2027},[609],"height:0.6833em;",[571,2029,732],{"className":2030,"style":901},[614,615],[571,2032],{"className":2033,"style":952},[926],[571,2035,776],{"className":2036},[959],[571,2038],{"className":2039,"style":952},[926],[571,2041,2043,2046],{"className":2042},[605],[571,2044],{"className":2045,"style":698},[609],[571,2047,2014],{"className":2048},[614],":",[571,2051,2053],{"className":2052},[706],[571,2054,2056,2133],{"className":2055},[574],[571,2057,2059],{"className":2058},[578],[580,2060,2061],{"xmlns":582,"display":715},[584,2062,2063,2130],{},[587,2064,2065,2067,2069,2072,2075,2078,2080,2082,2084,2098,2104,2106,2109,2111,2113,2115,2117,2119,2121,2123,2125,2127],{},[590,2066,1672],{},[633,2068,1675],{},[684,2070,2071],{},"101",[633,2073,2074],{},"≈",[684,2076,2077],{},"4,6151",[748,2079,758],{},[633,2081,761],{},[748,2083,758],{},[765,2085,2086,2088,2096],{},[633,2087,769],{},[587,2089,2090,2092,2094],{},[590,2091,639],{},[633,2093,776],{},[684,2095,686],{},[684,2097,2014],{},[1656,2099,2100,2102],{},[684,2101,686],{},[590,2103,639],{},[633,2105,2074],{},[684,2107,2108],{},"5,1874",[748,2110,758],{},[633,2112,761],{},[748,2114,758],{},[684,2116,686],{},[633,2118,735],{},[590,2120,1672],{},[633,2122,1675],{},[684,2124,2014],{},[633,2126,2074],{},[684,2128,2129],{},"5,6052",[594,2131,2132],{"encoding":596},"\\ln 101 \\approx 4{,}6151 \\;\\leq\\; \\sum_{n=1}^{100} \\frac{1}{n} \\approx 5{,}1874 \\;\\leq\\; 1 + \\ln 100 \\approx 5{,}6052",[571,2134,2136,2160,2198,2351,2386,2405,2429],{"className":2135,"ariaHidden":601},[600],[571,2137,2139,2142,2145,2148,2151,2154,2157],{"className":2138},[605],[571,2140],{"className":2141,"style":1857},[609],[571,2143,1672],{"className":2144},[843],[571,2146],{"className":2147,"style":927},[926],[571,2149,2071],{"className":2150},[614],[571,2152],{"className":2153,"style":952},[926],[571,2155,2074],{"className":2156},[959],[571,2158],{"className":2159,"style":952},[926],[571,2161,2163,2167,2171,2179,2183,2186,2189,2192,2195],{"className":2162},[605],[571,2164],{"className":2165,"style":2166},[609],"height:0.8389em;vertical-align:-0.1944em;",[571,2168,2170],{"className":2169},[614],"4",[571,2172,2174],{"className":2173},[614],[571,2175,2178],{"className":2176},[2177],"mpunct",",",[571,2180,2182],{"className":2181},[614],"6151",[571,2184],{"className":2185,"style":952},[926],[571,2187],{"className":2188,"style":952},[926],[571,2190,761],{"className":2191},[959],[571,2193],{"className":2194,"style":952},[926],[571,2196],{"className":2197,"style":952},[926],[571,2199,2201,2205,2273,2276,2342,2345,2348],{"className":2200},[605],[571,2202],{"className":2203,"style":2204},[609],"height:3.0682em;vertical-align:-1.2671em;",[571,2206,2208],{"className":2207},[843,976],[571,2209,2211,2265],{"className":2210},[857,858],[571,2212,2214,2262],{"className":2213},[862],[571,2215,2218,2238,2248],{"className":2216,"style":2217},[866],"height:1.8011em;",[571,2219,2220,2223],{"style":989},[571,2221],{"className":2222,"style":993},[874],[571,2224,2226],{"className":2225},[879,880,881,882],[571,2227,2229,2232,2235],{"className":2228},[614,882],[571,2230,639],{"className":2231},[614,615,882],[571,2233,776],{"className":2234},[959,882],[571,2236,686],{"className":2237},[614,882],[571,2239,2240,2243],{"style":1011},[571,2241],{"className":2242,"style":993},[874],[571,2244,2245],{},[571,2246,769],{"className":2247},[843,847,848],[571,2249,2250,2253],{"style":1022},[571,2251],{"className":2252,"style":993},[874],[571,2254,2256],{"className":2255},[879,880,881,882],[571,2257,2259],{"className":2258},[614,882],[571,2260,2014],{"className":2261},[614,882],[571,2263,913],{"className":2264},[912],[571,2266,2268],{"className":2267},[862],[571,2269,2271],{"className":2270,"style":1044},[866],[571,2272],{},[571,2274],{"className":2275,"style":927},[926],[571,2277,2279,2282,2339],{"className":2278},[614],[571,2280],{"className":2281},[662,1762],[571,2283,2285],{"className":2284},[1656],[571,2286,2288,2330],{"className":2287},[857,858],[571,2289,2291,2327],{"className":2290},[862],[571,2292,2295,2307,2315],{"className":2293,"style":2294},[866],"height:1.3214em;",[571,2296,2298,2301],{"style":2297},"top:-2.314em;",[571,2299],{"className":2300,"style":1782},[874],[571,2302,2304],{"className":2303},[614],[571,2305,639],{"className":2306},[614,615],[571,2308,2309,2312],{"style":1794},[571,2310],{"className":2311,"style":1782},[874],[571,2313],{"className":2314,"style":1802},[1801],[571,2316,2318,2321],{"style":2317},"top:-3.677em;",[571,2319],{"className":2320,"style":1782},[874],[571,2322,2324],{"className":2323},[614],[571,2325,686],{"className":2326},[614],[571,2328,913],{"className":2329},[912],[571,2331,2333],{"className":2332},[862],[571,2334,2337],{"className":2335,"style":2336},[866],"height:0.686em;",[571,2338],{},[571,2340],{"className":2341},[669,1762],[571,2343],{"className":2344,"style":952},[926],[571,2346,2074],{"className":2347},[959],[571,2349],{"className":2350,"style":952},[926],[571,2352,2354,2357,2361,2367,2371,2374,2377,2380,2383],{"className":2353},[605],[571,2355],{"className":2356,"style":2166},[609],[571,2358,2360],{"className":2359},[614],"5",[571,2362,2364],{"className":2363},[614],[571,2365,2178],{"className":2366},[2177],[571,2368,2370],{"className":2369},[614],"1874",[571,2372],{"className":2373,"style":952},[926],[571,2375],{"className":2376,"style":952},[926],[571,2378,761],{"className":2379},[959],[571,2381],{"className":2382,"style":952},[926],[571,2384],{"className":2385,"style":952},[926],[571,2387,2389,2393,2396,2399,2402],{"className":2388},[605],[571,2390],{"className":2391,"style":2392},[609],"height:0.7278em;vertical-align:-0.0833em;",[571,2394,686],{"className":2395},[614],[571,2397],{"className":2398,"style":1098},[926],[571,2400,735],{"className":2401},[905],[571,2403],{"className":2404,"style":1098},[926],[571,2406,2408,2411,2414,2417,2420,2423,2426],{"className":2407},[605],[571,2409],{"className":2410,"style":1857},[609],[571,2412,1672],{"className":2413},[843],[571,2415],{"className":2416,"style":927},[926],[571,2418,2014],{"className":2419},[614],[571,2421],{"className":2422,"style":952},[926],[571,2424,2074],{"className":2425},[959],[571,2427],{"className":2428,"style":952},[926],[571,2430,2432,2435,2438,2444],{"className":2431},[605],[571,2433],{"className":2434,"style":2166},[609],[571,2436,2360],{"className":2437},[614],[571,2439,2441],{"className":2440},[614],[571,2442,2178],{"className":2443},[2177],[571,2445,2447],{"className":2446},[614],"6052",[563,2449,2450,2661,2662,2786,2787,2843,2844,2922],{},[571,2451,2453,2494],{"className":2452},[574],[571,2454,2456],{"className":2455},[578],[580,2457,2458],{"xmlns":582},[584,2459,2460,2491],{},[587,2461,2462,2477],{},[721,2463,2464,2466,2475],{},[633,2465,769],{},[587,2467,2468,2470,2472],{},[590,2469,639],{},[633,2471,776],{},[684,2473,2474],{},"2",[590,2476,1229],{"mathvariant":1228},[1656,2478,2479,2481],{},[684,2480,686],{},[587,2482,2483,2485,2487,2489],{},[590,2484,639],{},[590,2486,1672],{},[633,2488,1675],{},[590,2490,639],{},[594,2492,2493],{"encoding":596},"\\sum_{n=2}^{\\infty} \\frac{1}{n \\ln n}",[571,2495,2497],{"className":2496,"ariaHidden":601},[600],[571,2498,2500,2503,2570,2573],{"className":2499},[605],[571,2501],{"className":2502,"style":1919},[609],[571,2504,2506,2509],{"className":2505},[843],[571,2507,769],{"className":2508,"style":1923},[843,847,1702],[571,2510,2512],{"className":2511},[853],[571,2513,2515,2561],{"className":2514},[857,858],[571,2516,2518,2558],{"className":2517},[862],[571,2519,2522,2543],{"className":2520,"style":2521},[866],"height:0.8043em;",[571,2523,2525,2528],{"style":2524},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[571,2526],{"className":2527,"style":875},[874],[571,2529,2531],{"className":2530},[879,880,881,882],[571,2532,2534,2537,2540],{"className":2533},[614,882],[571,2535,639],{"className":2536},[614,615,882],[571,2538,776],{"className":2539},[959,882],[571,2541,2474],{"className":2542},[614,882],[571,2544,2546,2549],{"style":2545},"top:-3.2029em;margin-right:0.05em;",[571,2547],{"className":2548,"style":875},[874],[571,2550,2552],{"className":2551},[879,880,881,882],[571,2553,2555],{"className":2554},[614,882],[571,2556,1229],{"className":2557},[614,882],[571,2559,913],{"className":2560},[912],[571,2562,2564],{"className":2563},[862],[571,2565,2568],{"className":2566,"style":2567},[866],"height:0.2997em;",[571,2569],{},[571,2571],{"className":2572,"style":927},[926],[571,2574,2576,2579,2658],{"className":2575},[614],[571,2577],{"className":2578},[662,1762],[571,2580,2582],{"className":2581},[1656],[571,2583,2585,2650],{"className":2584},[857,858],[571,2586,2588,2647],{"className":2587},[862],[571,2589,2591,2625,2633],{"className":2590,"style":1775},[866],[571,2592,2593,2596],{"style":1778},[571,2594],{"className":2595,"style":1782},[874],[571,2597,2599],{"className":2598},[879,880,881,882],[571,2600,2602,2605,2609,2619,2622],{"className":2601},[614,882],[571,2603,639],{"className":2604},[614,615,882],[571,2606],{"className":2607,"style":2608},[926,882],"margin-right:0.1952em;",[571,2610,2612,2616],{"className":2611},[843,882],[571,2613,2615],{"className":2614},[882],"l",[571,2617,639],{"className":2618},[882],[571,2620],{"className":2621,"style":2608},[926,882],[571,2623,639],{"className":2624},[614,615,882],[571,2626,2627,2630],{"style":1794},[571,2628],{"className":2629,"style":1782},[874],[571,2631],{"className":2632,"style":1802},[1801],[571,2634,2635,2638],{"style":1805},[571,2636],{"className":2637,"style":1782},[874],[571,2639,2641],{"className":2640},[879,880,881,882],[571,2642,2644],{"className":2643},[614,882],[571,2645,686],{"className":2646},[614,882],[571,2648,913],{"className":2649},[912],[571,2651,2653],{"className":2652},[862],[571,2654,2656],{"className":2655,"style":1827},[866],[571,2657],{},[571,2659],{"className":2660},[669,1762],": Eine Stammfunktion von ",[571,2663,2665,2691],{"className":2664},[574],[571,2666,2668],{"className":2667},[578],[580,2669,2670],{"xmlns":582},[584,2671,2672,2688],{},[587,2673,2674],{},[1656,2675,2676,2678],{},[684,2677,686],{},[587,2679,2680,2682,2684,2686],{},[590,2681,744],{},[590,2683,1672],{},[633,2685,1675],{},[590,2687,744],{},[594,2689,2690],{"encoding":596},"\\frac{1}{x \\ln x}",[571,2692,2694],{"className":2693,"ariaHidden":601},[600],[571,2695,2697,2700],{"className":2696},[605],[571,2698],{"className":2699,"style":1919},[609],[571,2701,2703,2706,2783],{"className":2702},[614],[571,2704],{"className":2705},[662,1762],[571,2707,2709],{"className":2708},[1656],[571,2710,2712,2775],{"className":2711},[857,858],[571,2713,2715,2772],{"className":2714},[862],[571,2716,2718,2750,2758],{"className":2717,"style":1775},[866],[571,2719,2720,2723],{"style":1778},[571,2721],{"className":2722,"style":1782},[874],[571,2724,2726],{"className":2725},[879,880,881,882],[571,2727,2729,2732,2735,2744,2747],{"className":2728},[614,882],[571,2730,744],{"className":2731},[614,615,882],[571,2733],{"className":2734,"style":2608},[926,882],[571,2736,2738,2741],{"className":2737},[843,882],[571,2739,2615],{"className":2740},[882],[571,2742,639],{"className":2743},[882],[571,2745],{"className":2746,"style":2608},[926,882],[571,2748,744],{"className":2749},[614,615,882],[571,2751,2752,2755],{"style":1794},[571,2753],{"className":2754,"style":1782},[874],[571,2756],{"className":2757,"style":1802},[1801],[571,2759,2760,2763],{"style":1805},[571,2761],{"className":2762,"style":1782},[874],[571,2764,2766],{"className":2765},[879,880,881,882],[571,2767,2769],{"className":2768},[614,882],[571,2770,686],{"className":2771},[614,882],[571,2773,913],{"className":2774},[912],[571,2776,2778],{"className":2777},[862],[571,2779,2781],{"className":2780,"style":1827},[866],[571,2782],{},[571,2784],{"className":2785},[669,1762]," ist ",[571,2788,2790,2816],{"className":2789},[574],[571,2791,2793],{"className":2792},[578],[580,2794,2795],{"xmlns":582},[584,2796,2797,2813],{},[587,2798,2799,2801,2803,2805,2807,2809,2811],{},[590,2800,1672],{},[633,2802,1675],{},[633,2804,636],{"stretchy":635},[590,2806,1672],{},[633,2808,1675],{},[590,2810,744],{},[633,2812,642],{"stretchy":635},[594,2814,2815],{"encoding":596},"\\ln(\\ln x)",[571,2817,2819],{"className":2818,"ariaHidden":601},[600],[571,2820,2822,2825,2828,2831,2834,2837,2840],{"className":2821},[605],[571,2823],{"className":2824,"style":655},[609],[571,2826,1672],{"className":2827},[843],[571,2829,636],{"className":2830},[662],[571,2832,1672],{"className":2833},[843],[571,2835],{"className":2836,"style":927},[926],[571,2838,744],{"className":2839},[614,615],[571,2841,642],{"className":2842},[669],", und ",[571,2845,2847,2877],{"className":2846},[574],[571,2848,2850],{"className":2849},[578],[580,2851,2852],{"xmlns":582},[584,2853,2854,2874],{},[587,2855,2856,2858,2860,2862,2864,2866,2868,2870,2872],{},[590,2857,1672],{},[633,2859,1675],{},[633,2861,636],{"stretchy":635},[590,2863,1672],{},[633,2865,1675],{},[590,2867,744],{},[633,2869,642],{"stretchy":635},[633,2871,1680],{},[590,2873,1229],{"mathvariant":1228},[594,2875,2876],{"encoding":596},"\\ln(\\ln x) \\to \\infty",[571,2878,2880,2913],{"className":2879,"ariaHidden":601},[600],[571,2881,2883,2886,2889,2892,2895,2898,2901,2904,2907,2910],{"className":2882},[605],[571,2884],{"className":2885,"style":655},[609],[571,2887,1672],{"className":2888},[843],[571,2890,636],{"className":2891},[662],[571,2893,1672],{"className":2894},[843],[571,2896],{"className":2897,"style":927},[926],[571,2899,744],{"className":2900},[614,615],[571,2902,642],{"className":2903},[669],[571,2905],{"className":2906,"style":952},[926],[571,2908,1680],{"className":2909},[959],[571,2911],{"className":2912,"style":952},[926],[571,2914,2916,2919],{"className":2915},[605],[571,2917],{"className":2918,"style":1882},[609],[571,2920,1229],{"className":2921},[614],". Die Reihe divergiert, wenn auch extrem langsam.",[563,2924,2925,1634,2928,3070,3071,3123,3124,3415,3416,3549,3550,3680,3681,3721],{},[567,2926,2927],{},"Rest von",[571,2929,2931,2956],{"className":2930},[574],[571,2932,2934],{"className":2933},[578],[580,2935,2936],{"xmlns":582},[584,2937,2938,2953],{},[587,2939,2940,2942],{},[633,2941,769],{},[1656,2943,2944,2946],{},[684,2945,686],{},[2947,2948,2949,2951],"msup",{},[590,2950,639],{},[684,2952,2474],{},[594,2954,2955],{"encoding":596},"\\sum \\frac{1}{n^2}",[571,2957,2959],{"className":2958,"ariaHidden":601},[600],[571,2960,2962,2965,2968,2971],{"className":2961},[605],[571,2963],{"className":2964,"style":1919},[609],[571,2966,769],{"className":2967,"style":1923},[843,847,1702],[571,2969],{"className":2970,"style":927},[926],[571,2972,2974,2977,3067],{"className":2973},[614],[571,2975],{"className":2976},[662,1762],[571,2978,2980],{"className":2979},[1656],[571,2981,2983,3059],{"className":2982},[857,858],[571,2984,2986,3056],{"className":2985},[862],[571,2987,2989,3034,3042],{"className":2988,"style":1775},[866],[571,2990,2991,2994],{"style":1778},[571,2992],{"className":2993,"style":1782},[874],[571,2995,2997],{"className":2996},[879,880,881,882],[571,2998,3000],{"className":2999},[614,882],[571,3001,3003,3006],{"className":3002},[614,882],[571,3004,639],{"className":3005},[614,615,882],[571,3007,3009],{"className":3008},[853],[571,3010,3012],{"className":3011},[857],[571,3013,3015],{"className":3014},[862],[571,3016,3019],{"className":3017,"style":3018},[866],"height:0.7463em;",[571,3020,3022,3026],{"style":3021},"top:-2.786em;margin-right:0.0714em;",[571,3023],{"className":3024,"style":3025},[874],"height:2.5em;",[571,3027,3031],{"className":3028},[879,3029,3030,882],"reset-size3","size1",[571,3032,2474],{"className":3033},[614,882],[571,3035,3036,3039],{"style":1794},[571,3037],{"className":3038,"style":1782},[874],[571,3040],{"className":3041,"style":1802},[1801],[571,3043,3044,3047],{"style":1805},[571,3045],{"className":3046,"style":1782},[874],[571,3048,3050],{"className":3049},[879,880,881,882],[571,3051,3053],{"className":3052},[614,882],[571,3054,686],{"className":3055},[614,882],[571,3057,913],{"className":3058},[912],[571,3060,3062],{"className":3061},[862],[571,3063,3065],{"className":3064,"style":1827},[866],[571,3066],{},[571,3068],{"className":3069},[669,1762]," nach ",[571,3072,3074,3093],{"className":3073},[574],[571,3075,3077],{"className":3076},[578],[580,3078,3079],{"xmlns":582},[584,3080,3081,3090],{},[587,3082,3083,3085,3087],{},[590,3084,732],{},[633,3086,776],{},[684,3088,3089],{},"10",[594,3091,3092],{"encoding":596},"N = 10",[571,3094,3096,3114],{"className":3095,"ariaHidden":601},[600],[571,3097,3099,3102,3105,3108,3111],{"className":3098},[605],[571,3100],{"className":3101,"style":2027},[609],[571,3103,732],{"className":3104,"style":901},[614,615],[571,3106],{"className":3107,"style":952},[926],[571,3109,776],{"className":3110},[959],[571,3112],{"className":3113,"style":952},[926],[571,3115,3117,3120],{"className":3116},[605],[571,3118],{"className":3119,"style":698},[609],[571,3121,3089],{"className":3122},[614]," Gliedern: Mit ",[571,3125,3127,3169],{"className":3126},[574],[571,3128,3130],{"className":3129},[578],[580,3131,3132],{"xmlns":582},[584,3133,3134,3166],{},[587,3135,3136,3144,3158,3160],{},[721,3137,3138,3140,3142],{},[633,3139,725],{},[590,3141,732],{},[590,3143,1229],{"mathvariant":1228},[1656,3145,3146,3152],{},[587,3147,3148,3150],{},[590,3149,753],{},[590,3151,744],{},[2947,3153,3154,3156],{},[590,3155,744],{},[684,3157,2474],{},[633,3159,776],{},[1656,3161,3162,3164],{},[684,3163,686],{},[590,3165,732],{},[594,3167,3168],{"encoding":596},"\\int_N^\\infty \\frac{dx}{x^2} = \\frac{1}{N}",[571,3170,3172,3341],{"className":3171,"ariaHidden":601},[600],[571,3173,3175,3179,3231,3234,3332,3335,3338],{"className":3174},[605],[571,3176],{"className":3177,"style":3178},[609],"height:1.2359em;vertical-align:-0.3558em;",[571,3180,3182,3185],{"className":3181},[843],[571,3183,725],{"className":3184,"style":1703},[843,847,1702],[571,3186,3188],{"className":3187},[853],[571,3189,3191,3223],{"className":3190},[857,858],[571,3192,3194,3220],{"className":3193},[862],[571,3195,3198,3209],{"className":3196,"style":3197},[866],"height:0.8593em;",[571,3199,3200,3203],{"style":1719},[571,3201],{"className":3202,"style":875},[874],[571,3204,3206],{"className":3205},[879,880,881,882],[571,3207,732],{"className":3208,"style":901},[614,615,882],[571,3210,3211,3214],{"style":1731},[571,3212],{"className":3213,"style":875},[874],[571,3215,3217],{"className":3216},[879,880,881,882],[571,3218,1229],{"className":3219},[614,882],[571,3221,913],{"className":3222},[912],[571,3224,3226],{"className":3225},[862],[571,3227,3229],{"className":3228,"style":1750},[866],[571,3230],{},[571,3232],{"className":3233,"style":927},[926],[571,3235,3237,3240,3329],{"className":3236},[614],[571,3238],{"className":3239},[662,1762],[571,3241,3243],{"className":3242},[1656],[571,3244,3246,3321],{"className":3245},[857,858],[571,3247,3249,3318],{"className":3248},[862],[571,3250,3253,3293,3301],{"className":3251,"style":3252},[866],"height:0.8801em;",[571,3254,3255,3258],{"style":1778},[571,3256],{"className":3257,"style":1782},[874],[571,3259,3261],{"className":3260},[879,880,881,882],[571,3262,3264],{"className":3263},[614,882],[571,3265,3267,3270],{"className":3266},[614,882],[571,3268,744],{"className":3269},[614,615,882],[571,3271,3273],{"className":3272},[853],[571,3274,3276],{"className":3275},[857],[571,3277,3279],{"className":3278},[862],[571,3280,3282],{"className":3281,"style":3018},[866],[571,3283,3284,3287],{"style":3021},[571,3285],{"className":3286,"style":3025},[874],[571,3288,3290],{"className":3289},[879,3029,3030,882],[571,3291,2474],{"className":3292},[614,882],[571,3294,3295,3298],{"style":1794},[571,3296],{"className":3297,"style":1782},[874],[571,3299],{"className":3300,"style":1802},[1801],[571,3302,3303,3306],{"style":1805},[571,3304],{"className":3305,"style":1782},[874],[571,3307,3309],{"className":3308},[879,880,881,882],[571,3310,3312,3315],{"className":3311},[614,882],[571,3313,753],{"className":3314},[614,615,882],[571,3316,744],{"className":3317},[614,615,882],[571,3319,913],{"className":3320},[912],[571,3322,3324],{"className":3323},[862],[571,3325,3327],{"className":3326,"style":1827},[866],[571,3328],{},[571,3330],{"className":3331},[669,1762],[571,3333],{"className":3334,"style":952},[926],[571,3336,776],{"className":3337},[959],[571,3339],{"className":3340,"style":952},[926],[571,3342,3344,3347],{"className":3343},[605],[571,3345],{"className":3346,"style":1919},[609],[571,3348,3350,3353,3412],{"className":3349},[614],[571,3351],{"className":3352},[662,1762],[571,3354,3356],{"className":3355},[1656],[571,3357,3359,3404],{"className":3358},[857,858],[571,3360,3362,3401],{"className":3361},[862],[571,3363,3365,3379,3387],{"className":3364,"style":1775},[866],[571,3366,3367,3370],{"style":1778},[571,3368],{"className":3369,"style":1782},[874],[571,3371,3373],{"className":3372},[879,880,881,882],[571,3374,3376],{"className":3375},[614,882],[571,3377,732],{"className":3378,"style":901},[614,615,882],[571,3380,3381,3384],{"style":1794},[571,3382],{"className":3383,"style":1782},[874],[571,3385],{"className":3386,"style":1802},[1801],[571,3388,3389,3392],{"style":1805},[571,3390],{"className":3391,"style":1782},[874],[571,3393,3395],{"className":3394},[879,880,881,882],[571,3396,3398],{"className":3397},[614,882],[571,3399,686],{"className":3400},[614,882],[571,3402,913],{"className":3403},[912],[571,3405,3407],{"className":3406},[862],[571,3408,3410],{"className":3409,"style":1827},[866],[571,3411],{},[571,3413],{"className":3414},[669,1762]," liegt der Rest zwischen ",[571,3417,3419,3443],{"className":3418},[574],[571,3420,3422],{"className":3421},[578],[580,3423,3424],{"xmlns":582},[584,3425,3426,3440],{},[587,3427,3428,3435,3437],{},[1656,3429,3430,3432],{},[684,3431,686],{},[684,3433,3434],{},"11",[633,3436,2074],{},[684,3438,3439],{},"0,0909",[594,3441,3442],{"encoding":596},"\\frac{1}{11} \\approx 0{,}0909",[571,3444,3446,3529],{"className":3445,"ariaHidden":601},[600],[571,3447,3449,3452,3520,3523,3526],{"className":3448},[605],[571,3450],{"className":3451,"style":1919},[609],[571,3453,3455,3458,3517],{"className":3454},[614],[571,3456],{"className":3457},[662,1762],[571,3459,3461],{"className":3460},[1656],[571,3462,3464,3509],{"className":3463},[857,858],[571,3465,3467,3506],{"className":3466},[862],[571,3468,3470,3484,3492],{"className":3469,"style":1775},[866],[571,3471,3472,3475],{"style":1778},[571,3473],{"className":3474,"style":1782},[874],[571,3476,3478],{"className":3477},[879,880,881,882],[571,3479,3481],{"className":3480},[614,882],[571,3482,3434],{"className":3483},[614,882],[571,3485,3486,3489],{"style":1794},[571,3487],{"className":3488,"style":1782},[874],[571,3490],{"className":3491,"style":1802},[1801],[571,3493,3494,3497],{"style":1805},[571,3495],{"className":3496,"style":1782},[874],[571,3498,3500],{"className":3499},[879,880,881,882],[571,3501,3503],{"className":3502},[614,882],[571,3504,686],{"className":3505},[614,882],[571,3507,913],{"className":3508},[912],[571,3510,3512],{"className":3511},[862],[571,3513,3515],{"className":3514,"style":1827},[866],[571,3516],{},[571,3518],{"className":3519},[669,1762],[571,3521],{"className":3522,"style":952},[926],[571,3524,2074],{"className":3525},[959],[571,3527],{"className":3528,"style":952},[926],[571,3530,3532,3535,3539,3545],{"className":3531},[605],[571,3533],{"className":3534,"style":2166},[609],[571,3536,3538],{"className":3537},[614],"0",[571,3540,3542],{"className":3541},[614],[571,3543,2178],{"className":3544},[2177],[571,3546,3548],{"className":3547},[614],"0909"," und ",[571,3551,3553,3576],{"className":3552},[574],[571,3554,3556],{"className":3555},[578],[580,3557,3558],{"xmlns":582},[584,3559,3560,3573],{},[587,3561,3562,3568,3570],{},[1656,3563,3564,3566],{},[684,3565,686],{},[684,3567,3089],{},[633,3569,776],{},[684,3571,3572],{},"0,1",[594,3574,3575],{"encoding":596},"\\frac{1}{10} = 0{,}1",[571,3577,3579,3662],{"className":3578,"ariaHidden":601},[600],[571,3580,3582,3585,3653,3656,3659],{"className":3581},[605],[571,3583],{"className":3584,"style":1919},[609],[571,3586,3588,3591,3650],{"className":3587},[614],[571,3589],{"className":3590},[662,1762],[571,3592,3594],{"className":3593},[1656],[571,3595,3597,3642],{"className":3596},[857,858],[571,3598,3600,3639],{"className":3599},[862],[571,3601,3603,3617,3625],{"className":3602,"style":1775},[866],[571,3604,3605,3608],{"style":1778},[571,3606],{"className":3607,"style":1782},[874],[571,3609,3611],{"className":3610},[879,880,881,882],[571,3612,3614],{"className":3613},[614,882],[571,3615,3089],{"className":3616},[614,882],[571,3618,3619,3622],{"style":1794},[571,3620],{"className":3621,"style":1782},[874],[571,3623],{"className":3624,"style":1802},[1801],[571,3626,3627,3630],{"style":1805},[571,3628],{"className":3629,"style":1782},[874],[571,3631,3633],{"className":3632},[879,880,881,882],[571,3634,3636],{"className":3635},[614,882],[571,3637,686],{"className":3638},[614,882],[571,3640,913],{"className":3641},[912],[571,3643,3645],{"className":3644},[862],[571,3646,3648],{"className":3647,"style":1827},[866],[571,3649],{},[571,3651],{"className":3652},[669,1762],[571,3654],{"className":3655,"style":952},[926],[571,3657,776],{"className":3658},[959],[571,3660],{"className":3661,"style":952},[926],[571,3663,3665,3668,3671,3677],{"className":3664},[605],[571,3666],{"className":3667,"style":2166},[609],[571,3669,3538],{"className":3670},[614],[571,3672,3674],{"className":3673},[614],[571,3675,2178],{"className":3676},[2177],[571,3678,686],{"className":3679},[614],". Tatsächlich ist er etwa ",[571,3682,3684,3699],{"className":3683},[574],[571,3685,3687],{"className":3686},[578],[580,3688,3689],{"xmlns":582},[584,3690,3691,3696],{},[587,3692,3693],{},[684,3694,3695],{},"0,0952",[594,3697,3698],{"encoding":596},"0{,}0952",[571,3700,3702],{"className":3701,"ariaHidden":601},[600],[571,3703,3705,3708,3711,3717],{"className":3704},[605],[571,3706],{"className":3707,"style":2166},[609],[571,3709,3538],{"className":3710},[614],[571,3712,3714],{"className":3713},[614],[571,3715,2178],{"className":3716},[2177],[571,3718,3720],{"className":3719},[614],"0952",".",[558,3723,3725],{"id":3724},"typische-fehler","Typische Fehler",[3727,3728,3729,4324,4327],"ul",{},[3730,3731,3732,3733,3952,3953,4319,4320,4323],"li",{},"Den Reihenwert mit dem Integralwert gleichsetzen. ",[571,3734,3736,3774],{"className":3735},[574],[571,3737,3739],{"className":3738},[578],[580,3740,3741],{"xmlns":582},[584,3742,3743,3771],{},[587,3744,3745,3753,3767,3769],{},[721,3746,3747,3749,3751],{},[633,3748,725],{},[684,3750,686],{},[590,3752,1229],{"mathvariant":1228},[1656,3754,3755,3761],{},[587,3756,3757,3759],{},[590,3758,753],{},[590,3760,744],{},[2947,3762,3763,3765],{},[590,3764,744],{},[684,3766,2474],{},[633,3768,776],{},[684,3770,686],{},[594,3772,3773],{"encoding":596},"\\int_1^\\infty \\frac{dx}{x^2} = 1",[571,3775,3777,3943],{"className":3776,"ariaHidden":601},[600],[571,3778,3780,3783,3834,3837,3934,3937,3940],{"className":3779},[605],[571,3781],{"className":3782,"style":3178},[609],[571,3784,3786,3789],{"className":3785},[843],[571,3787,725],{"className":3788,"style":1703},[843,847,1702],[571,3790,3792],{"className":3791},[853],[571,3793,3795,3826],{"className":3794},[857,858],[571,3796,3798,3823],{"className":3797},[862],[571,3799,3801,3812],{"className":3800,"style":3197},[866],[571,3802,3803,3806],{"style":1719},[571,3804],{"className":3805,"style":875},[874],[571,3807,3809],{"className":3808},[879,880,881,882],[571,3810,686],{"className":3811},[614,882],[571,3813,3814,3817],{"style":1731},[571,3815],{"className":3816,"style":875},[874],[571,3818,3820],{"className":3819},[879,880,881,882],[571,3821,1229],{"className":3822},[614,882],[571,3824,913],{"className":3825},[912],[571,3827,3829],{"className":3828},[862],[571,3830,3832],{"className":3831,"style":1750},[866],[571,3833],{},[571,3835],{"className":3836,"style":927},[926],[571,3838,3840,3843,3931],{"className":3839},[614],[571,3841],{"className":3842},[662,1762],[571,3844,3846],{"className":3845},[1656],[571,3847,3849,3923],{"className":3848},[857,858],[571,3850,3852,3920],{"className":3851},[862],[571,3853,3855,3895,3903],{"className":3854,"style":3252},[866],[571,3856,3857,3860],{"style":1778},[571,3858],{"className":3859,"style":1782},[874],[571,3861,3863],{"className":3862},[879,880,881,882],[571,3864,3866],{"className":3865},[614,882],[571,3867,3869,3872],{"className":3868},[614,882],[571,3870,744],{"className":3871},[614,615,882],[571,3873,3875],{"className":3874},[853],[571,3876,3878],{"className":3877},[857],[571,3879,3881],{"className":3880},[862],[571,3882,3884],{"className":3883,"style":3018},[866],[571,3885,3886,3889],{"style":3021},[571,3887],{"className":3888,"style":3025},[874],[571,3890,3892],{"className":3891},[879,3029,3030,882],[571,3893,2474],{"className":3894},[614,882],[571,3896,3897,3900],{"style":1794},[571,3898],{"className":3899,"style":1782},[874],[571,3901],{"className":3902,"style":1802},[1801],[571,3904,3905,3908],{"style":1805},[571,3906],{"className":3907,"style":1782},[874],[571,3909,3911],{"className":3910},[879,880,881,882],[571,3912,3914,3917],{"className":3913},[614,882],[571,3915,753],{"className":3916},[614,615,882],[571,3918,744],{"className":3919},[614,615,882],[571,3921,913],{"className":3922},[912],[571,3924,3926],{"className":3925},[862],[571,3927,3929],{"className":3928,"style":1827},[866],[571,3930],{},[571,3932],{"className":3933},[669,1762],[571,3935],{"className":3936,"style":952},[926],[571,3938,776],{"className":3939},[959],[571,3941],{"className":3942,"style":952},[926],[571,3944,3946,3949],{"className":3945},[605],[571,3947],{"className":3948,"style":698},[609],[571,3950,686],{"className":3951},[614],", aber ",[571,3954,3956,4011],{"className":3955},[574],[571,3957,3959],{"className":3958},[578],[580,3960,3961],{"xmlns":582},[584,3962,3963,4008],{},[587,3964,3965,3979,3989,3991,4003,4005],{},[721,3966,3967,3969,3977],{},[633,3968,769],{},[587,3970,3971,3973,3975],{},[590,3972,639],{},[633,3974,776],{},[684,3976,686],{},[590,3978,1229],{"mathvariant":1228},[1656,3980,3981,3983],{},[684,3982,686],{},[2947,3984,3985,3987],{},[590,3986,639],{},[684,3988,2474],{},[633,3990,776],{},[1656,3992,3993,4000],{},[2947,3994,3995,3998],{},[590,3996,3997],{},"π",[684,3999,2474],{},[684,4001,4002],{},"6",[633,4004,2074],{},[684,4006,4007],{},"1,645",[594,4009,4010],{"encoding":596},"\\sum_{n=1}^\\infty \\frac{1}{n^2} = \\frac{\\pi^2}{6} \\approx 1{,}645",[571,4012,4014,4186,4300],{"className":4013,"ariaHidden":601},[600],[571,4015,4017,4020,4080,4083,4177,4180,4183],{"className":4016},[605],[571,4018],{"className":4019,"style":1919},[609],[571,4021,4023,4026],{"className":4022},[843],[571,4024,769],{"className":4025,"style":1923},[843,847,1702],[571,4027,4029],{"className":4028},[853],[571,4030,4032,4072],{"className":4031},[857,858],[571,4033,4035,4069],{"className":4034},[862],[571,4036,4038,4058],{"className":4037,"style":2521},[866],[571,4039,4040,4043],{"style":2524},[571,4041],{"className":4042,"style":875},[874],[571,4044,4046],{"className":4045},[879,880,881,882],[571,4047,4049,4052,4055],{"className":4048},[614,882],[571,4050,639],{"className":4051},[614,615,882],[571,4053,776],{"className":4054},[959,882],[571,4056,686],{"className":4057},[614,882],[571,4059,4060,4063],{"style":2545},[571,4061],{"className":4062,"style":875},[874],[571,4064,4066],{"className":4065},[879,880,881,882],[571,4067,1229],{"className":4068},[614,882],[571,4070,913],{"className":4071},[912],[571,4073,4075],{"className":4074},[862],[571,4076,4078],{"className":4077,"style":2567},[866],[571,4079],{},[571,4081],{"className":4082,"style":927},[926],[571,4084,4086,4089,4174],{"className":4085},[614],[571,4087],{"className":4088},[662,1762],[571,4090,4092],{"className":4091},[1656],[571,4093,4095,4166],{"className":4094},[857,858],[571,4096,4098,4163],{"className":4097},[862],[571,4099,4101,4141,4149],{"className":4100,"style":1775},[866],[571,4102,4103,4106],{"style":1778},[571,4104],{"className":4105,"style":1782},[874],[571,4107,4109],{"className":4108},[879,880,881,882],[571,4110,4112],{"className":4111},[614,882],[571,4113,4115,4118],{"className":4114},[614,882],[571,4116,639],{"className":4117},[614,615,882],[571,4119,4121],{"className":4120},[853],[571,4122,4124],{"className":4123},[857],[571,4125,4127],{"className":4126},[862],[571,4128,4130],{"className":4129,"style":3018},[866],[571,4131,4132,4135],{"style":3021},[571,4133],{"className":4134,"style":3025},[874],[571,4136,4138],{"className":4137},[879,3029,3030,882],[571,4139,2474],{"className":4140},[614,882],[571,4142,4143,4146],{"style":1794},[571,4144],{"className":4145,"style":1782},[874],[571,4147],{"className":4148,"style":1802},[1801],[571,4150,4151,4154],{"style":1805},[571,4152],{"className":4153,"style":1782},[874],[571,4155,4157],{"className":4156},[879,880,881,882],[571,4158,4160],{"className":4159},[614,882],[571,4161,686],{"className":4162},[614,882],[571,4164,913],{"className":4165},[912],[571,4167,4169],{"className":4168},[862],[571,4170,4172],{"className":4171,"style":1827},[866],[571,4173],{},[571,4175],{"className":4176},[669,1762],[571,4178],{"className":4179,"style":952},[926],[571,4181,776],{"className":4182},[959],[571,4184],{"className":4185,"style":952},[926],[571,4187,4189,4193,4291,4294,4297],{"className":4188},[605],[571,4190],{"className":4191,"style":4192},[609],"height:1.3629em;vertical-align:-0.345em;",[571,4194,4196,4199,4288],{"className":4195},[614],[571,4197],{"className":4198},[662,1762],[571,4200,4202],{"className":4201},[1656],[571,4203,4205,4280],{"className":4204},[857,858],[571,4206,4208,4277],{"className":4207},[862],[571,4209,4212,4226,4234],{"className":4210,"style":4211},[866],"height:1.0179em;",[571,4213,4214,4217],{"style":1778},[571,4215],{"className":4216,"style":1782},[874],[571,4218,4220],{"className":4219},[879,880,881,882],[571,4221,4223],{"className":4222},[614,882],[571,4224,4002],{"className":4225},[614,882],[571,4227,4228,4231],{"style":1794},[571,4229],{"className":4230,"style":1782},[874],[571,4232],{"className":4233,"style":1802},[1801],[571,4235,4236,4239],{"style":1805},[571,4237],{"className":4238,"style":1782},[874],[571,4240,4242],{"className":4241},[879,880,881,882],[571,4243,4245],{"className":4244},[614,882],[571,4246,4248,4252],{"className":4247},[614,882],[571,4249,3997],{"className":4250,"style":4251},[614,615,882],"margin-right:0.0359em;",[571,4253,4255],{"className":4254},[853],[571,4256,4258],{"className":4257},[857],[571,4259,4261],{"className":4260},[862],[571,4262,4265],{"className":4263,"style":4264},[866],"height:0.8913em;",[571,4266,4268,4271],{"style":4267},"top:-2.931em;margin-right:0.0714em;",[571,4269],{"className":4270,"style":3025},[874],[571,4272,4274],{"className":4273},[879,3029,3030,882],[571,4275,2474],{"className":4276},[614,882],[571,4278,913],{"className":4279},[912],[571,4281,4283],{"className":4282},[862],[571,4284,4286],{"className":4285,"style":1827},[866],[571,4287],{},[571,4289],{"className":4290},[669,1762],[571,4292],{"className":4293,"style":952},[926],[571,4295,2074],{"className":4296},[959],[571,4298],{"className":4299,"style":952},[926],[571,4301,4303,4306,4309,4315],{"className":4302},[605],[571,4304],{"className":4305,"style":2166},[609],[571,4307,686],{"className":4308},[614],[571,4310,4312],{"className":4311},[614],[571,4313,2178],{"className":4314},[2177],[571,4316,4318],{"className":4317},[614],"645",". Das Kriterium sagt nur, ",[567,4321,4322],{},"ob"," die Reihe konvergiert.",[3730,4325,4326],{},"Die Monotonie nicht prüfen. Für nicht monotone Funktionen kann das Integral konvergieren, während die Reihe divergiert, oder umgekehrt.",[3730,4328,4329],{},"Das Kriterium auf Reihen mit wechselnden Vorzeichen anwenden. Dafür ist z.B. das Leibniz-Kriterium zuständig.",{"title":4331,"searchDepth":4332,"depth":4332,"links":4333},"",2,[4334,4335,4336],{"id":560,"depth":4332,"text":561},{"id":1627,"depth":4332,"text":1628},{"id":3724,"depth":4332,"text":3725},[4338,4341,4344,4347,4351,4354,4357,4360],{"lhs":4339,"rhs":4340},"round(sum(1 .\u002F (1:100)), 4)","5.1874",{"lhs":4342,"rhs":4343},"round(log(101), 4)","4.6151",{"lhs":4345,"rhs":4346},"round(1 + log(100), 4)","5.6052",{"lhs":4348,"rhs":3538,"where":4349},"round((log(log(x + 1e-5)) - log(log(x - 1e-5)))\u002F2e-5 - 1\u002F(x*log(x)), 6)",{"x":4350},3,{"lhs":4352,"rhs":4353},"round(pi^2\u002F6 - sum(1 .\u002F (1:10).^2), 4)","0.0952",{"lhs":4355,"rhs":4356},"round(1\u002F11, 4)","0.0909",{"lhs":4358,"rhs":4359},"1\u002F10","0.1",{"lhs":4361,"rhs":4362},"round(pi^2\u002F6, 3)","1.645","f: [1, \\infty) \\to \\mathbb{R} \\text{ stetig, nichtnegativ und monoton fallend}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmo>:\u003C\u002Fmo>\u003Cmo stretchy=\"false\">[\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>→\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f: [1, \\infty) \\to \\mathbb{R}\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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">[\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∞\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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:0.6889em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">stetig, nichtnegativ und monoton fallend\u003C\u002Fspan>",null,"md","integral-test","\\sum_{n=1}^{\\infty} f(n) \\text{ konvergiert} \\;\\Leftrightarrow\\; \\int_{1}^{\\infty} f(x)\\,dx \\text{ konvergiert}","\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>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> konvergiert\u003C\u002Fmtext>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⇔\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmsubsup>\u003Cmo>∫\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmsubsup>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi>d\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmtext> konvergiert\u003C\u002Fmtext>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\sum_{n=1}^{\\infty} f(n) \\text{ konvergiert} \\;\\Leftrightarrow\\; \\int_{1}^{\\infty} f(x)\\,dx \\text{ konvergiert}\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=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\"> konvergiert\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\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>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.3262em;vertical-align:-0.9119em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">\u003Cspan class=\"mop op-symbol large-op\" style=\"margin-right:0.4445em;position:relative;top:-0.0011em;\">∫\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.4143em;\">\u003Cspan style=\"top:-1.7881em;margin-left:-0.4445em;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 mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.8129em;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 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:0.9119em;\">\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 mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\"> konvergiert\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fintegralkriterium",[],[4376,4377,4378,4379],"improper-integral","p-series","harmonic-series","comparison-test",{"title":548,"description":4331},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fintegralkriterium","Bei positiven, monoton fallenden Gliedern f(n) konvergiert die Reihe genau dann, wenn das uneigentliche Integral von f konvergiert.",[4384,4385,4386,4387],"konvergenzkriterium","integral","reihe","uneigentliches integral",[4389,4392,4395],{"symbol":592,"meaning":4390,"symbolHtml":4391},"stetige, nichtnegative, monoton fallende Funktion mit f(n) als Reihengliedern","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">f\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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":639,"meaning":4393,"symbolHtml":4394},"Index der Reihenglieder","\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>",{"symbol":744,"meaning":4396,"symbolHtml":4397},"Integrationsvariable","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x\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\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","guDpeWVkz8JQ7HVnnd9Ar1jNfzKypC95bDX3BjSfgQM",[4400,4403,4406,4409],{"stem":4401,"title":4402,"category":101},"de\u002Fformulas\u002Fmath\u002Fcalculus\u002Funeigentliches-integral","Uneigentliches Integral",{"stem":4404,"title":4405,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fharmonische-reihe","Harmonische Reihe",{"stem":4407,"title":4408,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fmajorantenkriterium","Majoranten- und Minorantenkriterium",{"stem":4410,"title":4411,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fverallgemeinerte-harmonische-reihe","Konvergenz der Reihe 1\u002Fnᵖ",1793824264100]