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Sie wachsen über jede Grenze, allerdings extrem langsam, ungefähr wie der natürliche Logarithmus:",[572,972,975],{"className":973},[974],"katex-display",[572,976,978,1026],{"className":977},[575],[572,979,981],{"className":980},[579],[581,982,984],{"xmlns":583,"display":983},"block",[585,985,986,1023],{},[588,987,988,994,997,1000,1003,1005,1007,1010,1013,1016,1018,1020],{},[634,989,990,992],{},[637,991,639],{},[637,993,642],{},[644,995,996],{},"≈",[637,998,999],{},"ln",[644,1001,1002],{},"⁡",[637,1004,642],{},[644,1006,652],{},[637,1008,1009],{},"γ",[644,1011,1012],{"separator":602},",",[748,1014],{"width":1015},"2em",[637,1017,1009],{},[644,1019,996],{},[591,1021,1022],{},"0,5772",[595,1024,1025],{"encoding":597},"H_n \\approx \\ln n + \\gamma, \\qquad \\gamma \\approx 0{,}5772",[572,1027,1029,1084,1111,1145],{"className":1028,"ariaHidden":602},[601],[572,1030,1032,1035,1075,1078,1081],{"className":1031},[606],[572,1033],{"className":1034,"style":686},[610],[572,1036,1038,1041],{"className":1037},[615],[572,1039,639],{"className":1040,"style":694},[615,693],[572,1042,1044],{"className":1043},[698],[572,1045,1047,1067],{"className":1046},[702,703],[572,1048,1050,1064],{"className":1049},[707],[572,1051,1053],{"className":1052,"style":712},[711],[572,1054,1055,1058],{"style":715},[572,1056],{"className":1057,"style":720},[719],[572,1059,1061],{"className":1060},[724,725,726,727],[572,1062,642],{"className":1063},[615,693,727],[572,1065,735],{"className":1066},[734],[572,1068,1070],{"className":1069},[707],[572,1071,1073],{"className":1072,"style":742},[711],[572,1074],{},[572,1076],{"className":1077,"style":749},[748],[572,1079,996],{"className":1080},[753],[572,1082],{"className":1083,"style":749},[748],[572,1085,1087,1091,1095,1099,1102,1105,1108],{"className":1086},[606],[572,1088],{"className":1089,"style":1090},[610],"height:0.7778em;vertical-align:-0.0833em;",[572,1092,999],{"className":1093},[1094],"mop",[572,1096],{"className":1097,"style":1098},[748],"margin-right:0.1667em;",[572,1100,642],{"className":1101},[615,693],[572,1103],{"className":1104,"style":770},[748],[572,1106,652],{"className":1107},[774],[572,1109],{"className":1110,"style":770},[748],[572,1112,1114,1118,1122,1126,1130,1133,1136,1139,1142],{"className":1113},[606],[572,1115],{"className":1116,"style":1117},[610],"height:0.6776em;vertical-align:-0.1944em;",[572,1119,1009],{"className":1120,"style":1121},[615,693],"margin-right:0.0556em;",[572,1123,1012],{"className":1124},[1125],"mpunct",[572,1127],{"className":1128,"style":1129},[748],"margin-right:2em;",[572,1131],{"className":1132,"style":1098},[748],[572,1134,1009],{"className":1135,"style":1121},[615,693],[572,1137],{"className":1138,"style":749},[748],[572,1140,996],{"className":1141},[753],[572,1143],{"className":1144,"style":749},[748],[572,1146,1148,1152,1155,1161],{"className":1147},[606],[572,1149],{"className":1150,"style":1151},[610],"height:0.8389em;vertical-align:-0.1944em;",[572,1153,593],{"className":1154},[615],[572,1156,1158],{"className":1157},[615],[572,1159,1012],{"className":1160},[1125],[572,1162,1164],{"className":1163},[615],"5772",[563,1166,1167,1168,1198,1199,1202,1203,1330],{},"Dabei ist ",[572,1169,1171,1185],{"className":1170},[575],[572,1172,1174],{"className":1173},[579],[581,1175,1176],{"xmlns":583},[585,1177,1178,1182],{},[588,1179,1180],{},[637,1181,1009],{},[595,1183,1184],{"encoding":597},"\\gamma",[572,1186,1188],{"className":1187,"ariaHidden":602},[601],[572,1189,1191,1195],{"className":1190},[606],[572,1192],{"className":1193,"style":1194},[610],"height:0.625em;vertical-align:-0.1944em;",[572,1196,1009],{"className":1197,"style":1121},[615,693]," die ",[567,1200,1201],{},"Euler-Mascheroni-Konstante","; genauer gilt ",[572,1204,1206,1238],{"className":1205},[575],[572,1207,1209],{"className":1208},[579],[581,1210,1211],{"xmlns":583},[585,1212,1213,1235],{},[588,1214,1215,1221,1224,1226,1228,1230,1233],{},[634,1216,1217,1219],{},[637,1218,639],{},[637,1220,642],{},[644,1222,1223],{},"−",[637,1225,999],{},[644,1227,1002],{},[637,1229,642],{},[644,1231,1232],{},"→",[637,1234,1009],{},[595,1236,1237],{"encoding":597},"H_n - \\ln n \\to \\gamma",[572,1239,1241,1296,1321],{"className":1240,"ariaHidden":602},[601],[572,1242,1244,1247,1287,1290,1293],{"className":1243},[606],[572,1245],{"className":1246,"style":686},[610],[572,1248,1250,1253],{"className":1249},[615],[572,1251,639],{"className":1252,"style":694},[615,693],[572,1254,1256],{"className":1255},[698],[572,1257,1259,1279],{"className":1258},[702,703],[572,1260,1262,1276],{"className":1261},[707],[572,1263,1265],{"className":1264,"style":712},[711],[572,1266,1267,1270],{"style":715},[572,1268],{"className":1269,"style":720},[719],[572,1271,1273],{"className":1272},[724,725,726,727],[572,1274,642],{"className":1275},[615,693,727],[572,1277,735],{"className":1278},[734],[572,1280,1282],{"className":1281},[707],[572,1283,1285],{"className":1284,"style":742},[711],[572,1286],{},[572,1288],{"className":1289,"style":770},[748],[572,1291,1223],{"className":1292},[774],[572,1294],{"className":1295,"style":770},[748],[572,1297,1299,1303,1306,1309,1312,1315,1318],{"className":1298},[606],[572,1300],{"className":1301,"style":1302},[610],"height:0.6944em;",[572,1304,999],{"className":1305},[1094],[572,1307],{"className":1308,"style":1098},[748],[572,1310,642],{"className":1311},[615,693],[572,1313],{"className":1314,"style":749},[748],[572,1316,1232],{"className":1317},[753],[572,1319],{"className":1320,"style":749},[748],[572,1322,1324,1327],{"className":1323},[606],[572,1325],{"className":1326,"style":1194},[610],[572,1328,1009],{"className":1329,"style":1121},[615,693],".",[563,1332,1333],{},"Verwandte Reihen:",[1335,1336,1337,1809],"ul",{},[1338,1339,1340,1489,1490,1543,1544,1330],"li",{},[572,1341,1343,1371],{"className":1342},[575],[572,1344,1346],{"className":1345},[579],[581,1347,1348],{"xmlns":583},[585,1349,1350,1368],{},[588,1351,1352,1355],{},[644,1353,1354],{},"∑",[654,1356,1357,1359],{},[591,1358,649],{},[1360,1361,1362,1365],"msup",{},[637,1363,1364],{},"k",[637,1366,1367],{},"s",[595,1369,1370],{"encoding":597},"\\sum \\frac{1}{k^s}",[572,1372,1374],{"className":1373,"ariaHidden":602},[601],[572,1375,1377,1380,1386,1389],{"className":1376},[606],[572,1378],{"className":1379,"style":784},[610],[572,1381,1354],{"className":1382,"style":1385},[1094,1383,1384],"op-symbol","small-op","position:relative;top:0em;",[572,1387],{"className":1388,"style":1098},[748],[572,1390,1392,1395,1486],{"className":1391},[615],[572,1393],{"className":1394},[791,792],[572,1396,1398],{"className":1397},[654],[572,1399,1401,1478],{"className":1400},[702,703],[572,1402,1404,1475],{"className":1403},[707],[572,1405,1407,1453,1461],{"className":1406,"style":805},[711],[572,1408,1409,1412],{"style":808},[572,1410],{"className":1411,"style":812},[719],[572,1413,1415],{"className":1414},[724,725,726,727],[572,1416,1418],{"className":1417},[615,727],[572,1419,1421,1425],{"className":1420},[615,727],[572,1422,1364],{"className":1423,"style":1424},[615,693,727],"margin-right:0.0315em;",[572,1426,1428],{"className":1427},[698],[572,1429,1431],{"className":1430},[702],[572,1432,1434],{"className":1433},[707],[572,1435,1438],{"className":1436,"style":1437},[711],"height:0.5935em;",[572,1439,1441,1445],{"style":1440},"top:-2.786em;margin-right:0.0714em;",[572,1442],{"className":1443,"style":1444},[719],"height:2.5em;",[572,1446,1450],{"className":1447},[724,1448,1449,727],"reset-size3","size1",[572,1451,1367],{"className":1452},[615,693,727],[572,1454,1455,1458],{"style":824},[572,1456],{"className":1457,"style":812},[719],[572,1459],{"className":1460,"style":832},[831],[572,1462,1463,1466],{"style":835},[572,1464],{"className":1465,"style":812},[719],[572,1467,1469],{"className":1468},[724,725,726,727],[572,1470,1472],{"className":1471},[615,727],[572,1473,649],{"className":1474},[615,727],[572,1476,735],{"className":1477},[734],[572,1479,1481],{"className":1480},[707],[572,1482,1484],{"className":1483,"style":857},[711],[572,1485],{},[572,1487],{"className":1488},[863,792]," konvergiert genau für ",[572,1491,1493,1512],{"className":1492},[575],[572,1494,1496],{"className":1495},[579],[581,1497,1498],{"xmlns":583},[585,1499,1500,1509],{},[588,1501,1502,1504,1507],{},[637,1503,1367],{},[644,1505,1506],{},">",[591,1508,649],{},[595,1510,1511],{"encoding":597},"s > 1",[572,1513,1515,1534],{"className":1514,"ariaHidden":602},[601],[572,1516,1518,1522,1525,1528,1531],{"className":1517},[606],[572,1519],{"className":1520,"style":1521},[610],"height:0.5782em;vertical-align:-0.0391em;",[572,1523,1367],{"className":1524},[615,693],[572,1526],{"className":1527,"style":749},[748],[572,1529,1506],{"className":1530},[753],[572,1532],{"className":1533,"style":749},[748],[572,1535,1537,1540],{"className":1536},[606],[572,1538],{"className":1539,"style":611},[610],[572,1541,649],{"className":1542},[615],", z.B. ",[572,1545,1547,1585],{"className":1546},[575],[572,1548,1550],{"className":1549},[579],[581,1551,1552],{"xmlns":583},[585,1553,1554,1582],{},[588,1555,1556,1558,1568,1570],{},[644,1557,1354],{},[654,1559,1560,1562],{},[591,1561,649],{},[1360,1563,1564,1566],{},[637,1565,1364],{},[591,1567,660],{},[644,1569,646],{},[654,1571,1572,1579],{},[1360,1573,1574,1577],{},[637,1575,1576],{},"π",[591,1578,660],{},[591,1580,1581],{},"6",[595,1583,1584],{"encoding":597},"\\sum \\frac{1}{k^2} = \\frac{\\pi^2}{6}",[572,1586,1588,1704],{"className":1587,"ariaHidden":602},[601],[572,1589,1591,1594,1597,1600,1695,1698,1701],{"className":1590},[606],[572,1592],{"className":1593,"style":784},[610],[572,1595,1354],{"className":1596,"style":1385},[1094,1383,1384],[572,1598],{"className":1599,"style":1098},[748],[572,1601,1603,1606,1692],{"className":1602},[615],[572,1604],{"className":1605},[791,792],[572,1607,1609],{"className":1608},[654],[572,1610,1612,1684],{"className":1611},[702,703],[572,1613,1615,1681],{"className":1614},[707],[572,1616,1618,1659,1667],{"className":1617,"style":805},[711],[572,1619,1620,1623],{"style":808},[572,1621],{"className":1622,"style":812},[719],[572,1624,1626],{"className":1625},[724,725,726,727],[572,1627,1629],{"className":1628},[615,727],[572,1630,1632,1635],{"className":1631},[615,727],[572,1633,1364],{"className":1634,"style":1424},[615,693,727],[572,1636,1638],{"className":1637},[698],[572,1639,1641],{"className":1640},[702],[572,1642,1644],{"className":1643},[707],[572,1645,1648],{"className":1646,"style":1647},[711],"height:0.7463em;",[572,1649,1650,1653],{"style":1440},[572,1651],{"className":1652,"style":1444},[719],[572,1654,1656],{"className":1655},[724,1448,1449,727],[572,1657,660],{"className":1658},[615,727],[572,1660,1661,1664],{"style":824},[572,1662],{"className":1663,"style":812},[719],[572,1665],{"className":1666,"style":832},[831],[572,1668,1669,1672],{"style":835},[572,1670],{"className":1671,"style":812},[719],[572,1673,1675],{"className":1674},[724,725,726,727],[572,1676,1678],{"className":1677},[615,727],[572,1679,649],{"className":1680},[615,727],[572,1682,735],{"className":1683},[734],[572,1685,1687],{"className":1686},[707],[572,1688,1690],{"className":1689,"style":857},[711],[572,1691],{},[572,1693],{"className":1694},[863,792],[572,1696],{"className":1697,"style":749},[748],[572,1699,646],{"className":1700},[753],[572,1702],{"className":1703,"style":749},[748],[572,1705,1707,1711],{"className":1706},[606],[572,1708],{"className":1709,"style":1710},[610],"height:1.3629em;vertical-align:-0.345em;",[572,1712,1714,1717,1806],{"className":1713},[615],[572,1715],{"className":1716},[791,792],[572,1718,1720],{"className":1719},[654],[572,1721,1723,1798],{"className":1722},[702,703],[572,1724,1726,1795],{"className":1725},[707],[572,1727,1730,1744,1752],{"className":1728,"style":1729},[711],"height:1.0179em;",[572,1731,1732,1735],{"style":808},[572,1733],{"className":1734,"style":812},[719],[572,1736,1738],{"className":1737},[724,725,726,727],[572,1739,1741],{"className":1740},[615,727],[572,1742,1581],{"className":1743},[615,727],[572,1745,1746,1749],{"style":824},[572,1747],{"className":1748,"style":812},[719],[572,1750],{"className":1751,"style":832},[831],[572,1753,1754,1757],{"style":835},[572,1755],{"className":1756,"style":812},[719],[572,1758,1760],{"className":1759},[724,725,726,727],[572,1761,1763],{"className":1762},[615,727],[572,1764,1766,1770],{"className":1765},[615,727],[572,1767,1576],{"className":1768,"style":1769},[615,693,727],"margin-right:0.0359em;",[572,1771,1773],{"className":1772},[698],[572,1774,1776],{"className":1775},[702],[572,1777,1779],{"className":1778},[707],[572,1780,1783],{"className":1781,"style":1782},[711],"height:0.8913em;",[572,1784,1786,1789],{"style":1785},"top:-2.931em;margin-right:0.0714em;",[572,1787],{"className":1788,"style":1444},[719],[572,1790,1792],{"className":1791},[724,1448,1449,727],[572,1793,660],{"className":1794},[615,727],[572,1796,735],{"className":1797},[734],[572,1799,1801],{"className":1800},[707],[572,1802,1804],{"className":1803,"style":857},[711],[572,1805],{},[572,1807],{"className":1808},[863,792],[1338,1810,565,1811,1814,1815,2050,2051,1330],{},[567,1812,1813],{},"alternierende"," harmonische Reihe ",[572,1816,1818,1853],{"className":1817},[575],[572,1819,1821],{"className":1820},[579],[581,1822,1823],{"xmlns":583},[585,1824,1825,1850],{},[588,1826,1827,1829,1831,1837,1839,1846,1848],{},[591,1828,649],{},[644,1830,1223],{},[654,1832,1833,1835],{},[591,1834,649],{},[591,1836,660],{},[644,1838,652],{},[654,1840,1841,1843],{},[591,1842,649],{},[591,1844,1845],{},"3",[644,1847,1223],{},[644,1849,665],{},[595,1851,1852],{"encoding":597},"1 - \\frac{1}{2} + \\frac{1}{3} - \\ldots",[572,1854,1856,1874,1957,2040],{"className":1855,"ariaHidden":602},[601],[572,1857,1859,1862,1865,1868,1871],{"className":1858},[606],[572,1860],{"className":1861,"style":763},[610],[572,1863,649],{"className":1864},[615],[572,1866],{"className":1867,"style":770},[748],[572,1869,1223],{"className":1870},[774],[572,1872],{"className":1873,"style":770},[748],[572,1875,1877,1880,1948,1951,1954],{"className":1876},[606],[572,1878],{"className":1879,"style":784},[610],[572,1881,1883,1886,1945],{"className":1882},[615],[572,1884],{"className":1885},[791,792],[572,1887,1889],{"className":1888},[654],[572,1890,1892,1937],{"className":1891},[702,703],[572,1893,1895,1934],{"className":1894},[707],[572,1896,1898,1912,1920],{"className":1897,"style":805},[711],[572,1899,1900,1903],{"style":808},[572,1901],{"className":1902,"style":812},[719],[572,1904,1906],{"className":1905},[724,725,726,727],[572,1907,1909],{"className":1908},[615,727],[572,1910,660],{"className":1911},[615,727],[572,1913,1914,1917],{"style":824},[572,1915],{"className":1916,"style":812},[719],[572,1918],{"className":1919,"style":832},[831],[572,1921,1922,1925],{"style":835},[572,1923],{"className":1924,"style":812},[719],[572,1926,1928],{"className":1927},[724,725,726,727],[572,1929,1931],{"className":1930},[615,727],[572,1932,649],{"className":1933},[615,727],[572,1935,735],{"className":1936},[734],[572,1938,1940],{"className":1939},[707],[572,1941,1943],{"className":1942,"style":857},[711],[572,1944],{},[572,1946],{"className":1947},[863,792],[572,1949],{"className":1950,"style":770},[748],[572,1952,652],{"className":1953},[774],[572,1955],{"className":1956,"style":770},[748],[572,1958,1960,1963,2031,2034,2037],{"className":1959},[606],[572,1961],{"className":1962,"style":784},[610],[572,1964,1966,1969,2028],{"className":1965},[615],[572,1967],{"className":1968},[791,792],[572,1970,1972],{"className":1971},[654],[572,1973,1975,2020],{"className":1974},[702,703],[572,1976,1978,2017],{"className":1977},[707],[572,1979,1981,1995,2003],{"className":1980,"style":805},[711],[572,1982,1983,1986],{"style":808},[572,1984],{"className":1985,"style":812},[719],[572,1987,1989],{"className":1988},[724,725,726,727],[572,1990,1992],{"className":1991},[615,727],[572,1993,1845],{"className":1994},[615,727],[572,1996,1997,2000],{"style":824},[572,1998],{"className":1999,"style":812},[719],[572,2001],{"className":2002,"style":832},[831],[572,2004,2005,2008],{"style":835},[572,2006],{"className":2007,"style":812},[719],[572,2009,2011],{"className":2010},[724,725,726,727],[572,2012,2014],{"className":2013},[615,727],[572,2015,649],{"className":2016},[615,727],[572,2018,735],{"className":2019},[734],[572,2021,2023],{"className":2022},[707],[572,2024,2026],{"className":2025,"style":857},[711],[572,2027],{},[572,2029],{"className":2030},[863,792],[572,2032],{"className":2033,"style":770},[748],[572,2035,1223],{"className":2036},[774],[572,2038],{"className":2039,"style":770},[748],[572,2041,2043,2047],{"className":2042},[606],[572,2044],{"className":2045,"style":2046},[610],"height:0.123em;",[572,2048,665],{"className":2049},[883]," konvergiert nach dem Leibniz-Kriterium, und zwar gegen ",[572,2052,2054,2072],{"className":2053},[575],[572,2055,2057],{"className":2056},[579],[581,2058,2059],{"xmlns":583},[585,2060,2061,2069],{},[588,2062,2063,2065,2067],{},[637,2064,999],{},[644,2066,1002],{},[591,2068,660],{},[595,2070,2071],{"encoding":597},"\\ln 2",[572,2073,2075],{"className":2074,"ariaHidden":602},[601],[572,2076,2078,2081,2084,2087],{"className":2077},[606],[572,2079],{"className":2080,"style":1302},[610],[572,2082,999],{"className":2083},[1094],[572,2085],{"className":2086,"style":1098},[748],[572,2088,660],{"className":2089},[615],[563,2091,2092,2093,2121],{},"Quotienten- und Wurzelkriterium liefern hier den Grenzwert ",[572,2094,2096,2109],{"className":2095},[575],[572,2097,2099],{"className":2098},[579],[581,2100,2101],{"xmlns":583},[585,2102,2103,2107],{},[588,2104,2105],{},[591,2106,649],{},[595,2108,649],{"encoding":597},[572,2110,2112],{"className":2111,"ariaHidden":602},[601],[572,2113,2115,2118],{"className":2114},[606],[572,2116],{"className":2117,"style":611},[610],[572,2119,649],{"className":2120},[615]," und damit keine Entscheidung.",[558,2123,2125],{"id":2124},"herleitung","Herleitung",[563,2127,2128],{},"Man fasst die Glieder in Gruppen zusammen, deren Länge sich jeweils verdoppelt:",[572,2130,2132],{"className":2131},[974],[572,2133,2135,2303],{"className":2134},[575],[572,2136,2138],{"className":2137},[579],[581,2139,2140],{"xmlns":583,"display":983},[585,2141,2142,2300],{},[588,2143,2144,2146,2148,2154,2156,2200,2202,2248,2250,2296,2298],{},[591,2145,649],{},[644,2147,652],{},[654,2149,2150,2152],{},[591,2151,649],{},[591,2153,660],{},[644,2155,652],{},[2157,2158,2159,2181],"munder",{},[2157,2160,2161,2178],{},[588,2162,2163,2169,2171],{},[654,2164,2165,2167],{},[591,2166,649],{},[591,2168,1845],{},[644,2170,652],{},[654,2172,2173,2175],{},[591,2174,649],{},[591,2176,2177],{},"4",[644,2179,2180],{"stretchy":602},"⏟",[588,2182,2183,2186,2192,2194],{},[644,2184,2185],{},"≥",[654,2187,2188,2190],{},[591,2189,660],{},[591,2191,2177],{},[644,2193,646],{},[654,2195,2196,2198],{},[591,2197,649],{},[591,2199,660],{},[644,2201,652],{},[2157,2203,2204,2230],{},[2157,2205,2206,2228],{},[588,2207,2208,2215,2217,2219,2221],{},[654,2209,2210,2212],{},[591,2211,649],{},[591,2213,2214],{},"5",[644,2216,652],{},[644,2218,665],{},[644,2220,652],{},[654,2222,2223,2225],{},[591,2224,649],{},[591,2226,2227],{},"8",[644,2229,2180],{"stretchy":602},[588,2231,2232,2234,2240,2242],{},[644,2233,2185],{},[654,2235,2236,2238],{},[591,2237,2177],{},[591,2239,2227],{},[644,2241,646],{},[654,2243,2244,2246],{},[591,2245,649],{},[591,2247,660],{},[644,2249,652],{},[2157,2251,2252,2278],{},[2157,2253,2254,2276],{},[588,2255,2256,2263,2265,2267,2269],{},[654,2257,2258,2260],{},[591,2259,649],{},[591,2261,2262],{},"9",[644,2264,652],{},[644,2266,665],{},[644,2268,652],{},[654,2270,2271,2273],{},[591,2272,649],{},[591,2274,2275],{},"16",[644,2277,2180],{"stretchy":602},[588,2279,2280,2282,2288,2290],{},[644,2281,2185],{},[654,2283,2284,2286],{},[591,2285,2227],{},[591,2287,2275],{},[644,2289,646],{},[654,2291,2292,2294],{},[591,2293,649],{},[591,2295,660],{},[644,2297,652],{},[644,2299,665],{},[595,2301,2302],{"encoding":597},"1 + \\frac{1}{2} + \\underbrace{\\frac{1}{3} + \\frac{1}{4}}_{\\geq \\frac{2}{4} = \\frac{1}{2}} + \\underbrace{\\frac{1}{5} + \\ldots + \\frac{1}{8}}_{\\geq \\frac{4}{8} = \\frac{1}{2}} + \\underbrace{\\frac{1}{9} + \\ldots + \\frac{1}{16}}_{\\geq \\frac{8}{16} = \\frac{1}{2}} + \\ldots",[572,2304,2306,2324,2406,2829,3231,3633],{"className":2305,"ariaHidden":602},[601],[572,2307,2309,2312,2315,2318,2321],{"className":2308},[606],[572,2310],{"className":2311,"style":763},[610],[572,2313,649],{"className":2314},[615],[572,2316],{"className":2317,"style":770},[748],[572,2319,652],{"className":2320},[774],[572,2322],{"className":2323,"style":770},[748],[572,2325,2327,2331,2397,2400,2403],{"className":2326},[606],[572,2328],{"className":2329,"style":2330},[610],"height:2.0074em;vertical-align:-0.686em;",[572,2332,2334,2337,2394],{"className":2333},[615],[572,2335],{"className":2336},[791,792],[572,2338,2340],{"className":2339},[654],[572,2341,2343,2385],{"className":2342},[702,703],[572,2344,2346,2382],{"className":2345},[707],[572,2347,2350,2362,2370],{"className":2348,"style":2349},[711],"height:1.3214em;",[572,2351,2353,2356],{"style":2352},"top:-2.314em;",[572,2354],{"className":2355,"style":812},[719],[572,2357,2359],{"className":2358},[615],[572,2360,660],{"className":2361},[615],[572,2363,2364,2367],{"style":824},[572,2365],{"className":2366,"style":812},[719],[572,2368],{"className":2369,"style":832},[831],[572,2371,2373,2376],{"style":2372},"top:-3.677em;",[572,2374],{"className":2375,"style":812},[719],[572,2377,2379],{"className":2378},[615],[572,2380,649],{"className":2381},[615],[572,2383,735],{"className":2384},[734],[572,2386,2388],{"className":2387},[707],[572,2389,2392],{"className":2390,"style":2391},[711],"height:0.686em;",[572,2393],{},[572,2395],{"className":2396},[863,792],[572,2398],{"className":2399,"style":770},[748],[572,2401,652],{"className":2402},[774],[572,2404],{"className":2405,"style":770},[748],[572,2407,2409,2413,2820,2823,2826],{"className":2408},[606],[572,2410],{"className":2411,"style":2412},[610],"height:3.6873em;vertical-align:-2.3658em;",[572,2414,2416],{"className":2415},[883,2157],[572,2417,2419,2811],{"className":2418},[702,703],[572,2420,2422,2808],{"className":2421},[707],[572,2423,2425,2587],{"className":2424,"style":2349},[711],[572,2426,2428,2432],{"style":2427},"top:-1.1964em;",[572,2429],{"className":2430,"style":2431},[719],"height:3.3214em;",[572,2433,2435],{"className":2434},[724,725,726,727],[572,2436,2438,2441,2516,2519],{"className":2437},[615,727],[572,2439,2185],{"className":2440},[753,727],[572,2442,2444,2448,2513],{"className":2443},[615,727],[572,2445],{"className":2446},[791,792,724,1448,2447],"size6",[572,2449,2451],{"className":2450},[654],[572,2452,2454,2504],{"className":2453},[702,703],[572,2455,2457,2501],{"className":2456},[707],[572,2458,2461,2476,2486],{"className":2459,"style":2460},[711],"height:0.8443em;",[572,2462,2464,2467],{"style":2463},"top:-2.656em;",[572,2465],{"className":2466,"style":812},[719],[572,2468,2470],{"className":2469},[724,1448,1449,727],[572,2471,2473],{"className":2472},[615,727],[572,2474,2177],{"className":2475},[615,727],[572,2477,2479,2482],{"style":2478},"top:-3.2255em;",[572,2480],{"className":2481,"style":812},[719],[572,2483],{"className":2484,"style":2485},[831,727],"border-bottom-width:0.049em;",[572,2487,2489,2492],{"style":2488},"top:-3.384em;",[572,2490],{"className":2491,"style":812},[719],[572,2493,2495],{"className":2494},[724,1448,1449,727],[572,2496,2498],{"className":2497},[615,727],[572,2499,660],{"className":2500},[615,727],[572,2502,735],{"className":2503},[734],[572,2505,2507],{"className":2506},[707],[572,2508,2511],{"className":2509,"style":2510},[711],"height:0.344em;",[572,2512],{},[572,2514],{"className":2515},[863,792,724,1448,2447],[572,2517,646],{"className":2518},[753,727],[572,2520,2522,2525,2584],{"className":2521},[615,727],[572,2523],{"className":2524},[791,792,724,1448,2447],[572,2526,2528],{"className":2527},[654],[572,2529,2531,2576],{"className":2530},[702,703],[572,2532,2534,2573],{"className":2533},[707],[572,2535,2537,2551,2559],{"className":2536,"style":2460},[711],[572,2538,2539,2542],{"style":2463},[572,2540],{"className":2541,"style":812},[719],[572,2543,2545],{"className":2544},[724,1448,1449,727],[572,2546,2548],{"className":2547},[615,727],[572,2549,660],{"className":2550},[615,727],[572,2552,2553,2556],{"style":2478},[572,2554],{"className":2555,"style":812},[719],[572,2557],{"className":2558,"style":2485},[831,727],[572,2560,2561,2564],{"style":2488},[572,2562],{"className":2563,"style":812},[719],[572,2565,2567],{"className":2566},[724,1448,1449,727],[572,2568,2570],{"className":2569},[615,727],[572,2571,649],{"className":2572},[615,727],[572,2574,735],{"className":2575},[734],[572,2577,2579],{"className":2578},[707],[572,2580,2582],{"className":2581,"style":2510},[711],[572,2583],{},[572,2585],{"className":2586},[863,792,724,1448,2447],[572,2588,2590,2593],{"style":2589},"top:-3.3214em;",[572,2591],{"className":2592,"style":2431},[719],[572,2594,2596],{"className":2595},[883,2157],[572,2597,2599,2799],{"className":2598},[702,703],[572,2600,2602,2796],{"className":2601},[707],[572,2603,2605,2655],{"className":2604,"style":2349},[711],[572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1}",[572,3678,3680],{"className":3679,"ariaHidden":602},[601],[572,3681,3683,3687],{"className":3682},[606],[572,3684],{"className":3685,"style":3686},[610],"height:1.2484em;vertical-align:-0.4033em;",[572,3688,3690,3693,3785],{"className":3689},[615],[572,3691],{"className":3692},[791,792],[572,3694,3696],{"className":3695},[654],[572,3697,3699,3776],{"className":3698},[702,703],[572,3700,3702,3773],{"className":3701},[707],[572,3703,3705,3751,3759],{"className":3704,"style":805},[711],[572,3706,3707,3710],{"style":808},[572,3708],{"className":3709,"style":812},[719],[572,3711,3713],{"className":3712},[724,725,726,727],[572,3714,3716,3745,3748],{"className":3715},[615,727],[572,3717,3719,3722],{"className":3718},[615,727],[572,3720,660],{"className":3721},[615,727],[572,3723,3725],{"className":3724},[698],[572,3726,3728],{"className":3727},[702],[572,3729,3731],{"className":3730},[707],[572,3732,3734],{"className":3733,"style":1437},[711],[572,3735,3736,3739],{"style":1440},[572,3737],{"className":3738,"style":1444},[719],[572,3740,3742],{"className":3741},[724,1448,1449,727],[572,3743,3669],{"className":3744},[615,693,727],[572,3746,652],{"className":3747},[774,727],[572,3749,649],{"className":3750},[615,727],[572,3752,3753,3756],{"style":824},[572,3754],{"className":3755,"style":812},[719],[572,3757],{"className":3758,"style":832},[831],[572,3760,3761,3764],{"style":835},[572,3762],{"className":3763,"style":812},[719],[572,3765,3767],{"className":3766},[724,725,726,727],[572,3768,3770],{"className":3769},[615,727],[572,3771,649],{"className":3772},[615,727],[572,3774,735],{"className":3775},[734],[572,3777,3779],{"className":3778},[707],[572,3780,3783],{"className":3781,"style":3782},[711],"height:0.4033em;",[572,3784],{},[572,3786],{"className":3787},[863,792]," bis ",[572,3790,3792,3820],{"className":3791},[575],[572,3793,3795],{"className":3794},[579],[581,3796,3797],{"xmlns":583},[585,3798,3799,3817],{},[588,3800,3801],{},[654,3802,3803,3805],{},[591,3804,649],{},[1360,3806,3807,3809],{},[591,3808,660],{},[588,3810,3811,3813,3815],{},[637,3812,3669],{},[644,3814,652],{},[591,3816,649],{},[595,3818,3819],{"encoding":597},"\\frac{1}{2^{m+1}}",[572,3821,3823],{"className":3822,"ariaHidden":602},[601],[572,3824,3826,3829],{"className":3825},[606],[572,3827],{"className":3828,"style":784},[610],[572,3830,3832,3835,3929],{"className":3831},[615],[572,3833],{"className":3834},[791,792],[572,3836,3838],{"className":3837},[654],[572,3839,3841,3921],{"className":3840},[702,703],[572,3842,3844,3918],{"className":3843},[707],[572,3845,3847,3896,3904],{"className":3846,"style":805},[711],[572,3848,3849,3852],{"style":808},[572,3850],{"className":3851,"style":812},[719],[572,3853,3855],{"className":3854},[724,725,726,727],[572,3856,3858],{"className":3857},[615,727],[572,3859,3861,3864],{"className":3860},[615,727],[572,3862,660],{"className":3863},[615,727],[572,3865,3867],{"className":3866},[698],[572,3868,3870],{"className":3869},[702],[572,3871,3873],{"className":3872},[707],[572,3874,3876],{"className":3875,"style":1647},[711],[572,3877,3878,3881],{"style":1440},[572,3879],{"className":3880,"style":1444},[719],[572,3882,3884],{"className":3883},[724,1448,1449,727],[572,3885,3887,3890,3893],{"className":3886},[615,727],[572,3888,3669],{"className":3889},[615,693,727],[572,3891,652],{"className":3892},[774,727],[572,3894,649],{"className":3895},[615,727],[572,3897,3898,3901],{"style":824},[572,3899],{"className":3900,"style":812},[719],[572,3902],{"className":3903,"style":832},[831],[572,3905,3906,3909],{"style":835},[572,3907],{"className":3908,"style":812},[719],[572,3910,3912],{"className":3911},[724,725,726,727],[572,3913,3915],{"className":3914},[615,727],[572,3916,649],{"className":3917},[615,727],[572,3919,735],{"className":3920},[734],[572,3922,3924],{"className":3923},[707],[572,3925,3927],{"className":3926,"style":857},[711],[572,3928],{},[572,3930],{"className":3931},[863,792]," hat ",[572,3934,3936,3954],{"className":3935},[575],[572,3937,3939],{"className":3938},[579],[581,3940,3941],{"xmlns":583},[585,3942,3943,3951],{},[588,3944,3945],{},[1360,3946,3947,3949],{},[591,3948,660],{},[637,3950,3669],{},[595,3952,3953],{"encoding":597},"2^m",[572,3955,3957],{"className":3956,"ariaHidden":602},[601],[572,3958,3960,3964],{"className":3959},[606],[572,3961],{"className":3962,"style":3963},[610],"height:0.6644em;",[572,3965,3967,3970],{"className":3966},[615],[572,3968,660],{"className":3969},[615],[572,3971,3973],{"className":3972},[698],[572,3974,3976],{"className":3975},[702],[572,3977,3979],{"className":3978},[707],[572,3980,3982],{"className":3981,"style":3963},[711],[572,3983,3985,3988],{"style":3984},"top:-3.063em;margin-right:0.05em;",[572,3986],{"className":3987,"style":720},[719],[572,3989,3991],{"className":3990},[724,725,726,727],[572,3992,3669],{"className":3993},[615,693,727]," Glieder, jedes mindestens ",[572,3996,3998,4025],{"className":3997},[575],[572,3999,4001],{"className":4000},[579],[581,4002,4003],{"xmlns":583},[585,4004,4005,4023],{},[588,4006,4007],{},[654,4008,4009,4011],{},[591,4010,649],{},[1360,4012,4013,4015],{},[591,4014,660],{},[588,4016,4017,4019,4021],{},[637,4018,3669],{},[644,4020,652],{},[591,4022,649],{},[595,4024,3819],{"encoding":597},[572,4026,4028],{"className":4027,"ariaHidden":602},[601],[572,4029,4031,4034],{"className":4030},[606],[572,4032],{"className":4033,"style":784},[610],[572,4035,4037,4040,4134],{"className":4036},[615],[572,4038],{"className":4039},[791,792],[572,4041,4043],{"className":4042},[654],[572,4044,4046,4126],{"className":4045},[702,703],[572,4047,4049,4123],{"className":4048},[707],[572,4050,4052,4101,4109],{"className":4051,"style":805},[711],[572,4053,4054,4057],{"style":808},[572,4055],{"className":4056,"style":812},[719],[572,4058,4060],{"className":4059},[724,725,726,727],[572,4061,4063],{"className":4062},[615,727],[572,4064,4066,4069],{"className":4065},[615,727],[572,4067,660],{"className":4068},[615,727],[572,4070,4072],{"className":4071},[698],[572,4073,4075],{"className":4074},[702],[572,4076,4078],{"className":4077},[707],[572,4079,4081],{"className":4080,"style":1647},[711],[572,4082,4083,4086],{"style":1440},[572,4084],{"className":4085,"style":1444},[719],[572,4087,4089],{"className":4088},[724,1448,1449,727],[572,4090,4092,4095,4098],{"className":4091},[615,727],[572,4093,3669],{"className":4094},[615,693,727],[572,4096,652],{"className":4097},[774,727],[572,4099,649],{"className":4100},[615,727],[572,4102,4103,4106],{"style":824},[572,4104],{"className":4105,"style":812},[719],[572,4107],{"className":4108,"style":832},[831],[572,4110,4111,4114],{"style":835},[572,4112],{"className":4113,"style":812},[719],[572,4115,4117],{"className":4116},[724,725,726,727],[572,4118,4120],{"className":4119},[615,727],[572,4121,649],{"className":4122},[615,727],[572,4124,735],{"className":4125},[734],[572,4127,4129],{"className":4128},[707],[572,4130,4132],{"className":4131,"style":857},[711],[572,4133],{},[572,4135],{"className":4136},[863,792],", und ist damit mindestens ",[572,4139,4141,4159],{"className":4140},[575],[572,4142,4144],{"className":4143},[579],[581,4145,4146],{"xmlns":583},[585,4147,4148,4156],{},[588,4149,4150],{},[654,4151,4152,4154],{},[591,4153,649],{},[591,4155,660],{},[595,4157,4158],{"encoding":597},"\\frac{1}{2}",[572,4160,4162],{"className":4161,"ariaHidden":602},[601],[572,4163,4165,4168],{"className":4164},[606],[572,4166],{"className":4167,"style":784},[610],[572,4169,4171,4174,4233],{"className":4170},[615],[572,4172],{"className":4173},[791,792],[572,4175,4177],{"className":4176},[654],[572,4178,4180,4225],{"className":4179},[702,703],[572,4181,4183,4222],{"className":4182},[707],[572,4184,4186,4200,4208],{"className":4185,"style":805},[711],[572,4187,4188,4191],{"style":808},[572,4189],{"className":4190,"style":812},[719],[572,4192,4194],{"className":4193},[724,725,726,727],[572,4195,4197],{"className":4196},[615,727],[572,4198,660],{"className":4199},[615,727],[572,4201,4202,4205],{"style":824},[572,4203],{"className":4204,"style":812},[719],[572,4206],{"className":4207,"style":832},[831],[572,4209,4210,4213],{"style":835},[572,4211],{"className":4212,"style":812},[719],[572,4214,4216],{"className":4215},[724,725,726,727],[572,4217,4219],{"className":4218},[615,727],[572,4220,649],{"className":4221},[615,727],[572,4223,735],{"className":4224},[734],[572,4226,4228],{"className":4227},[707],[572,4229,4231],{"className":4230,"style":857},[711],[572,4232],{},[572,4234],{"className":4235},[863,792],". Also gilt ",[572,4238,4240,4274],{"className":4239},[575],[572,4241,4243],{"className":4242},[579],[581,4244,4245],{"xmlns":583},[585,4246,4247,4271],{},[588,4248,4249,4259,4261,4263,4265],{},[634,4250,4251,4253],{},[637,4252,639],{},[1360,4254,4255,4257],{},[591,4256,660],{},[637,4258,3669],{},[644,4260,2185],{},[591,4262,649],{},[644,4264,652],{},[654,4266,4267,4269],{},[637,4268,3669],{},[591,4270,660],{},[595,4272,4273],{"encoding":597},"H_{2^m} \\geq 1 + \\frac{m}{2}",[572,4275,4277,4362,4380],{"className":4276,"ariaHidden":602},[601],[572,4278,4280,4283,4353,4356,4359],{"className":4279},[606],[572,4281],{"className":4282,"style":686},[610],[572,4284,4286,4289],{"className":4285},[615],[572,4287,639],{"className":4288,"style":694},[615,693],[572,4290,4292],{"className":4291},[698],[572,4293,4295,4345],{"className":4294},[702,703],[572,4296,4298,4342],{"className":4297},[707],[572,4299,4302],{"className":4300,"style":4301},[711],"height:0.3011em;",[572,4303,4304,4307],{"style":715},[572,4305],{"className":4306,"style":720},[719],[572,4308,4310],{"className":4309},[724,725,726,727],[572,4311,4313],{"className":4312},[615,727],[572,4314,4316,4319],{"className":4315},[615,727],[572,4317,660],{"className":4318},[615,727],[572,4320,4322],{"className":4321},[698],[572,4323,4325],{"className":4324},[702],[572,4326,4328],{"className":4327},[707],[572,4329,4331],{"className":4330,"style":1437},[711],[572,4332,4333,4336],{"style":1440},[572,4334],{"className":4335,"style":1444},[719],[572,4337,4339],{"className":4338},[724,1448,1449,727],[572,4340,3669],{"className":4341},[615,693,727],[572,4343,735],{"className":4344},[734],[572,4346,4348],{"className":4347},[707],[572,4349,4351],{"className":4350,"style":742},[711],[572,4352],{},[572,4354],{"className":4355,"style":749},[748],[572,4357,2185],{"className":4358},[753],[572,4360],{"className":4361,"style":749},[748],[572,4363,4365,4368,4371,4374,4377],{"className":4364},[606],[572,4366],{"className":4367,"style":763},[610],[572,4369,649],{"className":4370},[615],[572,4372],{"className":4373,"style":770},[748],[572,4375,652],{"className":4376},[774],[572,4378],{"className":4379,"style":770},[748],[572,4381,4383,4387],{"className":4382},[606],[572,4384],{"className":4385,"style":4386},[610],"height:1.0404em;vertical-align:-0.345em;",[572,4388,4390,4393,4453],{"className":4389},[615],[572,4391],{"className":4392},[791,792],[572,4394,4396],{"className":4395},[654],[572,4397,4399,4445],{"className":4398},[702,703],[572,4400,4402,4442],{"className":4401},[707],[572,4403,4406,4420,4428],{"className":4404,"style":4405},[711],"height:0.6954em;",[572,4407,4408,4411],{"style":808},[572,4409],{"className":4410,"style":812},[719],[572,4412,4414],{"className":4413},[724,725,726,727],[572,4415,4417],{"className":4416},[615,727],[572,4418,660],{"className":4419},[615,727],[572,4421,4422,4425],{"style":824},[572,4423],{"className":4424,"style":812},[719],[572,4426],{"className":4427,"style":832},[831],[572,4429,4430,4433],{"style":835},[572,4431],{"className":4432,"style":812},[719],[572,4434,4436],{"className":4435},[724,725,726,727],[572,4437,4439],{"className":4438},[615,727],[572,4440,3669],{"className":4441},[615,693,727],[572,4443,735],{"className":4444},[734],[572,4446,4448],{"className":4447},[707],[572,4449,4451],{"className":4450,"style":857},[711],[572,4452],{},[572,4454],{"className":4455},[863,792],", und das wächst über jede Grenze.",[558,4458,4460],{"id":4459},"beispiele","Beispiele",[563,4462,4463],{},"Die ersten Partialsummen:",[572,4465,4467],{"className":4466},[974],[572,4468,4470,4551],{"className":4469},[575],[572,4471,4473],{"className":4472},[579],[581,4474,4475],{"xmlns":583,"display":983},[585,4476,4477,4548],{},[588,4478,4479,4485,4487,4495,4497,4499,4505,4507,4515,4517,4520,4522,4524,4526,4532,4534,4536,4543,4545],{},[634,4480,4481,4483],{},[637,4482,639],{},[591,4484,2177],{},[644,4486,646],{},[654,4488,4489,4492],{},[591,4490,4491],{},"25",[591,4493,4494],{},"12",[644,4496,1012],{"separator":602},[748,4498],{"width":1015},[634,4500,4501,4503],{},[637,4502,639],{},[591,4504,2227],{},[644,4506,646],{},[654,4508,4509,4512],{},[591,4510,4511],{},"761",[591,4513,4514],{},"280",[644,4516,996],{},[591,4518,4519],{},"2,7179",[644,4521,2185],{},[591,4523,649],{},[644,4525,652],{},[654,4527,4528,4530],{},[591,4529,1845],{},[591,4531,660],{},[644,4533,1012],{"separator":602},[748,4535],{"width":1015},[634,4537,4538,4540],{},[637,4539,639],{},[591,4541,4542],{},"10",[644,4544,996],{},[591,4546,4547],{},"2,929",[595,4549,4550],{"encoding":597},"H_4 = \\frac{25}{12}, \\qquad H_8 = \\frac{761}{280} \\approx 2{,}7179 \\geq 1 + \\frac{3}{2}, \\qquad H_{10} \\approx 2{,}929",[572,4552,4554,4609,4735,4812,4840,4858,4987],{"className":4553,"ariaHidden":602},[601],[572,4555,4557,4560,4600,4603,4606],{"className":4556},[606],[572,4558],{"className":4559,"style":686},[610],[572,4561,4563,4566],{"className":4562},[615],[572,4564,639],{"className":4565,"style":694},[615,693],[572,4567,4569],{"className":4568},[698],[572,4570,4572,4592],{"className":4571},[702,703],[572,4573,4575,4589],{"className":4574},[707],[572,4576,4578],{"className":4577,"style":4301},[711],[572,4579,4580,4583],{"style":715},[572,4581],{"className":4582,"style":720},[719],[572,4584,4586],{"className":4585},[724,725,726,727],[572,4587,2177],{"className":4588},[615,727],[572,4590,735],{"className":4591},[734],[572,4593,4595],{"className":4594},[707],[572,4596,4598],{"className":4597,"style":742},[711],[572,4599],{},[572,4601],{"className":4602,"style":749},[748],[572,4604,646],{"className":4605},[753],[572,4607],{"className":4608,"style":749},[748],[572,4610,4612,4615,4677,4680,4683,4686,4726,4729,4732],{"className":4611},[606],[572,4613],{"className":4614,"style":2330},[610],[572,4616,4618,4621,4674],{"className":4617},[615],[572,4619],{"className":4620},[791,792],[572,4622,4624],{"className":4623},[654],[572,4625,4627,4666],{"className":4626},[702,703],[572,4628,4630,4663],{"className":4629},[707],[572,4631,4633,4644,4652],{"className":4632,"style":2349},[711],[572,4634,4635,4638],{"style":2352},[572,4636],{"className":4637,"style":812},[719],[572,4639,4641],{"className":4640},[615],[572,4642,4494],{"className":4643},[615],[572,4645,4646,4649],{"style":824},[572,4647],{"className":4648,"style":812},[719],[572,4650],{"className":4651,"style":832},[831],[572,4653,4654,4657],{"style":2372},[572,4655],{"className":4656,"style":812},[719],[572,4658,4660],{"className":4659},[615],[572,4661,4491],{"className":4662},[615],[572,4664,735],{"className":4665},[734],[572,4667,4669],{"className":4668},[707],[572,4670,4672],{"className":4671,"style":2391},[711],[572,4673],{},[572,4675],{"className":4676},[863,792],[572,4678,1012],{"className":4679},[1125],[572,4681],{"className":4682,"style":1129},[748],[572,4684],{"className":4685,"style":1098},[748],[572,4687,4689,4692],{"className":4688},[615],[572,4690,639],{"className":4691,"style":694},[615,693],[572,4693,4695],{"className":4694},[698],[572,4696,4698,4718],{"className":4697},[702,703],[572,4699,4701,4715],{"className":4700},[707],[572,4702,4704],{"className":4703,"style":4301},[711],[572,4705,4706,4709],{"style":715},[572,4707],{"className":4708,"style":720},[719],[572,4710,4712],{"className":4711},[724,725,726,727],[572,4713,2227],{"className":4714},[615,727],[572,4716,735],{"className":4717},[734],[572,4719,4721],{"className":4720},[707],[572,4722,4724],{"className":4723,"style":742},[711],[572,4725],{},[572,4727],{"className":4728,"style":749},[748],[572,4730,646],{"className":4731},[753],[572,4733],{"className":4734,"style":749},[748],[572,4736,4738,4741,4803,4806,4809],{"className":4737},[606],[572,4739],{"className":4740,"style":2330},[610],[572,4742,4744,4747,4800],{"className":4743},[615],[572,4745],{"className":4746},[791,792],[572,4748,4750],{"className":4749},[654],[572,4751,4753,4792],{"className":4752},[702,703],[572,4754,4756,4789],{"className":4755},[707],[572,4757,4759,4770,4778],{"className":4758,"style":2349},[711],[572,4760,4761,4764],{"style":2352},[572,4762],{"className":4763,"style":812},[719],[572,4765,4767],{"className":4766},[615],[572,4768,4514],{"className":4769},[615],[572,4771,4772,4775],{"style":824},[572,4773],{"className":4774,"style":812},[719],[572,4776],{"className":4777,"style":832},[831],[572,4779,4780,4783],{"style":2372},[572,4781],{"className":4782,"style":812},[719],[572,4784,4786],{"className":4785},[615],[572,4787,4511],{"className":4788},[615],[572,4790,735],{"className":4791},[734],[572,4793,4795],{"className":4794},[707],[572,4796,4798],{"className":4797,"style":2391},[711],[572,4799],{},[572,4801],{"className":4802},[863,792],[572,4804],{"className":4805,"style":749},[748],[572,4807,996],{"className":4808},[753],[572,4810],{"className":4811,"style":749},[748],[572,4813,4815,4818,4821,4827,4831,4834,4837],{"className":4814},[606],[572,4816],{"className":4817,"style":1151},[610],[572,4819,660],{"className":4820},[615],[572,4822,4824],{"className":4823},[615],[572,4825,1012],{"className":4826},[1125],[572,4828,4830],{"className":4829},[615],"7179",[572,4832],{"className":4833,"style":749},[748],[572,4835,2185],{"className":4836},[753],[572,4838],{"className":4839,"style":749},[748],[572,4841,4843,4846,4849,4852,4855],{"className":4842},[606],[572,4844],{"className":4845,"style":763},[610],[572,4847,649],{"className":4848},[615],[572,4850],{"className":4851,"style":770},[748],[572,4853,652],{"className":4854},[774],[572,4856],{"className":4857,"style":770},[748],[572,4859,4861,4864,4926,4929,4932,4935,4978,4981,4984],{"className":4860},[606],[572,4862],{"className":4863,"style":2330},[610],[572,4865,4867,4870,4923],{"className":4866},[615],[572,4868],{"className":4869},[791,792],[572,4871,4873],{"className":4872},[654],[572,4874,4876,4915],{"className":4875},[702,703],[572,4877,4879,4912],{"className":4878},[707],[572,4880,4882,4893,4901],{"className":4881,"style":2349},[711],[572,4883,4884,4887],{"style":2352},[572,4885],{"className":4886,"style":812},[719],[572,4888,4890],{"className":4889},[615],[572,4891,660],{"className":4892},[615],[572,4894,4895,4898],{"style":824},[572,4896],{"className":4897,"style":812},[719],[572,4899],{"className":4900,"style":832},[831],[572,4902,4903,4906],{"style":2372},[572,4904],{"className":4905,"style":812},[719],[572,4907,4909],{"className":4908},[615],[572,4910,1845],{"className":4911},[615],[572,4913,735],{"className":4914},[734],[572,4916,4918],{"className":4917},[707],[572,4919,4921],{"className":4920,"style":2391},[711],[572,4922],{},[572,4924],{"className":4925},[863,792],[572,4927,1012],{"className":4928},[1125],[572,4930],{"className":4931,"style":1129},[748],[572,4933],{"className":4934,"style":1098},[748],[572,4936,4938,4941],{"className":4937},[615],[572,4939,639],{"className":4940,"style":694},[615,693],[572,4942,4944],{"className":4943},[698],[572,4945,4947,4970],{"className":4946},[702,703],[572,4948,4950,4967],{"className":4949},[707],[572,4951,4953],{"className":4952,"style":4301},[711],[572,4954,4955,4958],{"style":715},[572,4956],{"className":4957,"style":720},[719],[572,4959,4961],{"className":4960},[724,725,726,727],[572,4962,4964],{"className":4963},[615,727],[572,4965,4542],{"className":4966},[615,727],[572,4968,735],{"className":4969},[734],[572,4971,4973],{"className":4972},[707],[572,4974,4976],{"className":4975,"style":742},[711],[572,4977],{},[572,4979],{"className":4980,"style":749},[748],[572,4982,996],{"className":4983},[753],[572,4985],{"className":4986,"style":749},[748],[572,4988,4990,4993,4996,5002],{"className":4989},[606],[572,4991],{"className":4992,"style":1151},[610],[572,4994,660],{"className":4995},[615],[572,4997,4999],{"className":4998},[615],[572,5000,1012],{"className":5001},[1125],[572,5003,5005],{"className":5004},[615],"929",[563,5007,5008,5009,5062,5063,5133,5134,1330],{},"Für ",[572,5010,5012,5031],{"className":5011},[575],[572,5013,5015],{"className":5014},[579],[581,5016,5017],{"xmlns":583},[585,5018,5019,5028],{},[588,5020,5021,5023,5025],{},[637,5022,642],{},[644,5024,646],{},[591,5026,5027],{},"1000",[595,5029,5030],{"encoding":597},"n = 1000",[572,5032,5034,5053],{"className":5033,"ariaHidden":602},[601],[572,5035,5037,5041,5044,5047,5050],{"className":5036},[606],[572,5038],{"className":5039,"style":5040},[610],"height:0.4306em;",[572,5042,642],{"className":5043},[615,693],[572,5045],{"className":5046,"style":749},[748],[572,5048,646],{"className":5049},[753],[572,5051],{"className":5052,"style":749},[748],[572,5054,5056,5059],{"className":5055},[606],[572,5057],{"className":5058,"style":611},[610],[572,5060,5027],{"className":5061},[615]," liefern die Summe und die Näherung ",[572,5064,5066,5088],{"className":5065},[575],[572,5067,5069],{"className":5068},[579],[581,5070,5071],{"xmlns":583},[585,5072,5073,5085],{},[588,5074,5075,5077,5079,5081,5083],{},[637,5076,999],{},[644,5078,1002],{},[591,5080,5027],{},[644,5082,652],{},[591,5084,1022],{},[595,5086,5087],{"encoding":597},"\\ln 1000 + 0{,}5772",[572,5089,5091,5115],{"className":5090,"ariaHidden":602},[601],[572,5092,5094,5097,5100,5103,5106,5109,5112],{"className":5093},[606],[572,5095],{"className":5096,"style":1090},[610],[572,5098,999],{"className":5099},[1094],[572,5101],{"className":5102,"style":1098},[748],[572,5104,5027],{"className":5105},[615],[572,5107],{"className":5108,"style":770},[748],[572,5110,652],{"className":5111},[774],[572,5113],{"className":5114,"style":770},[748],[572,5116,5118,5121,5124,5130],{"className":5117},[606],[572,5119],{"className":5120,"style":1151},[610],[572,5122,593],{"className":5123},[615],[572,5125,5127],{"className":5126},[615],[572,5128,1012],{"className":5129},[1125],[572,5131,1164],{"className":5132},[615]," beide etwa ",[572,5135,5137,5152],{"className":5136},[575],[572,5138,5140],{"className":5139},[579],[581,5141,5142],{"xmlns":583},[585,5143,5144,5149],{},[588,5145,5146],{},[591,5147,5148],{},"7,485",[595,5150,5151],{"encoding":597},"7{,}485",[572,5153,5155],{"className":5154,"ariaHidden":602},[601],[572,5156,5158,5161,5165,5171],{"className":5157},[606],[572,5159],{"className":5160,"style":1151},[610],[572,5162,5164],{"className":5163},[615],"7",[572,5166,5168],{"className":5167},[615],[572,5169,1012],{"className":5170},[1125],[572,5172,5174],{"className":5173},[615],"485",[563,5176,5177,5178,5248,5249,5278,5279,5452],{},"Damit ",[572,5179,5181,5199],{"className":5180},[575],[572,5182,5184],{"className":5183},[579],[581,5185,5186],{"xmlns":583},[585,5187,5188,5196],{},[588,5189,5190],{},[634,5191,5192,5194],{},[637,5193,639],{},[637,5195,642],{},[595,5197,5198],{"encoding":597},"H_n",[572,5200,5202],{"className":5201,"ariaHidden":602},[601],[572,5203,5205,5208],{"className":5204},[606],[572,5206],{"className":5207,"style":686},[610],[572,5209,5211,5214],{"className":5210},[615],[572,5212,639],{"className":5213,"style":694},[615,693],[572,5215,5217],{"className":5216},[698],[572,5218,5220,5240],{"className":5219},[702,703],[572,5221,5223,5237],{"className":5222},[707],[572,5224,5226],{"className":5225,"style":712},[711],[572,5227,5228,5231],{"style":715},[572,5229],{"className":5230,"style":720},[719],[572,5232,5234],{"className":5233},[724,725,726,727],[572,5235,642],{"className":5236},[615,693,727],[572,5238,735],{"className":5239},[734],[572,5241,5243],{"className":5242},[707],[572,5244,5246],{"className":5245,"style":742},[711],[572,5247],{}," größer als ",[572,5250,5252,5266],{"className":5251},[575],[572,5253,5255],{"className":5254},[579],[581,5256,5257],{"xmlns":583},[585,5258,5259,5264],{},[588,5260,5261],{},[591,5262,5263],{},"20",[595,5265,5263],{"encoding":597},[572,5267,5269],{"className":5268,"ariaHidden":602},[601],[572,5270,5272,5275],{"className":5271},[606],[572,5273],{"className":5274,"style":611},[610],[572,5276,5263],{"className":5277},[615]," wird, braucht man nach der Näherung etwa ",[572,5280,5282,5321],{"className":5281},[575],[572,5283,5285],{"className":5284},[579],[581,5286,5287],{"xmlns":583},[585,5288,5289,5318],{},[588,5290,5291,5304,5306,5309,5312],{},[1360,5292,5293,5296],{},[637,5294,5295],{},"e",[588,5297,5298,5300,5302],{},[591,5299,5263],{},[644,5301,1223],{},[591,5303,1022],{},[644,5305,996],{},[591,5307,5308],{},"2,7",[644,5310,5311],{},"⋅",[1360,5313,5314,5316],{},[591,5315,4542],{},[591,5317,2227],{},[595,5319,5320],{"encoding":597},"e^{20 - 0{,}5772} \\approx 2{,}7 \\cdot 10^8",[572,5322,5324,5387,5414],{"className":5323,"ariaHidden":602},[601],[572,5325,5327,5331,5378,5381,5384],{"className":5326},[606],[572,5328],{"className":5329,"style":5330},[610],"height:0.8141em;",[572,5332,5334,5337],{"className":5333},[615],[572,5335,5295],{"className":5336},[615,693],[572,5338,5340],{"className":5339},[698],[572,5341,5343],{"className":5342},[702],[572,5344,5346],{"className":5345},[707],[572,5347,5349],{"className":5348,"style":5330},[711],[572,5350,5351,5354],{"style":3984},[572,5352],{"className":5353,"style":720},[719],[572,5355,5357],{"className":5356},[724,725,726,727],[572,5358,5360,5363,5366,5369,5375],{"className":5359},[615,727],[572,5361,5263],{"className":5362},[615,727],[572,5364,1223],{"className":5365},[774,727],[572,5367,593],{"className":5368},[615,727],[572,5370,5372],{"className":5371},[615,727],[572,5373,1012],{"className":5374},[1125,727],[572,5376,1164],{"className":5377},[615,727],[572,5379],{"className":5380,"style":749},[748],[572,5382,996],{"className":5383},[753],[572,5385],{"className":5386,"style":749},[748],[572,5388,5390,5393,5396,5402,5405,5408,5411],{"className":5389},[606],[572,5391],{"className":5392,"style":1151},[610],[572,5394,660],{"className":5395},[615],[572,5397,5399],{"className":5398},[615],[572,5400,1012],{"className":5401},[1125],[572,5403,5164],{"className":5404},[615],[572,5406],{"className":5407,"style":770},[748],[572,5409,5311],{"className":5410},[774],[572,5412],{"className":5413,"style":770},[748],[572,5415,5417,5420,5423],{"className":5416},[606],[572,5418],{"className":5419,"style":5330},[610],[572,5421,649],{"className":5422},[615],[572,5424,5426,5429],{"className":5425},[615],[572,5427,593],{"className":5428},[615],[572,5430,5432],{"className":5431},[698],[572,5433,5435],{"className":5434},[702],[572,5436,5438],{"className":5437},[707],[572,5439,5441],{"className":5440,"style":5330},[711],[572,5442,5443,5446],{"style":3984},[572,5444],{"className":5445,"style":720},[719],[572,5447,5449],{"className":5448},[724,725,726,727],[572,5450,2227],{"className":5451},[615,727]," Glieder.",[558,5454,5456],{"id":5455},"typische-fehler","Typische Fehler",[1335,5458,5459,5583,5586,5726],{},[1338,5460,5461,5462,5582],{},"Aus ",[572,5463,5465,5487],{"className":5464},[575],[572,5466,5468],{"className":5467},[579],[581,5469,5470],{"xmlns":583},[585,5471,5472,5484],{},[588,5473,5474,5480,5482],{},[654,5475,5476,5478],{},[591,5477,649],{},[637,5479,1364],{},[644,5481,1232],{},[591,5483,593],{},[595,5485,5486],{"encoding":597},"\\frac{1}{k} \\to 0",[572,5488,5490,5573],{"className":5489,"ariaHidden":602},[601],[572,5491,5493,5496,5564,5567,5570],{"className":5492},[606],[572,5494],{"className":5495,"style":784},[610],[572,5497,5499,5502,5561],{"className":5498},[615],[572,5500],{"className":5501},[791,792],[572,5503,5505],{"className":5504},[654],[572,5506,5508,5553],{"className":5507},[702,703],[572,5509,5511,5550],{"className":5510},[707],[572,5512,5514,5528,5536],{"className":5513,"style":805},[711],[572,5515,5516,5519],{"style":808},[572,5517],{"className":5518,"style":812},[719],[572,5520,5522],{"className":5521},[724,725,726,727],[572,5523,5525],{"className":5524},[615,727],[572,5526,1364],{"className":5527,"style":1424},[615,693,727],[572,5529,5530,5533],{"style":824},[572,5531],{"className":5532,"style":812},[719],[572,5534],{"className":5535,"style":832},[831],[572,5537,5538,5541],{"style":835},[572,5539],{"className":5540,"style":812},[719],[572,5542,5544],{"className":5543},[724,725,726,727],[572,5545,5547],{"className":5546},[615,727],[572,5548,649],{"className":5549},[615,727],[572,5551,735],{"className":5552},[734],[572,5554,5556],{"className":5555},[707],[572,5557,5559],{"className":5558,"style":857},[711],[572,5560],{},[572,5562],{"className":5563},[863,792],[572,5565],{"className":5566,"style":749},[748],[572,5568,1232],{"className":5569},[753],[572,5571],{"className":5572,"style":749},[748],[572,5574,5576,5579],{"className":5575},[606],[572,5577],{"className":5578,"style":611},[610],[572,5580,593],{"className":5581},[615]," auf Konvergenz schließen. Dass die Glieder eine Nullfolge bilden, ist nur notwendig, nicht hinreichend.",[1338,5584,5585],{},"Am Computer „Konvergenz beobachten“, weil die Partialsummen kaum noch wachsen. Das Wachstum ist logarithmisch, aber unbeschränkt.",[1338,5587,5588,5589,5725],{},"Die harmonische Reihe mit ",[572,5590,5592,5616],{"className":5591},[575],[572,5593,5595],{"className":5594},[579],[581,5596,5597],{"xmlns":583},[585,5598,5599,5613],{},[588,5600,5601,5603],{},[644,5602,1354],{},[654,5604,5605,5607],{},[591,5606,649],{},[1360,5608,5609,5611],{},[637,5610,1364],{},[591,5612,660],{},[595,5614,5615],{"encoding":597},"\\sum \\frac{1}{k^2}",[572,5617,5619],{"className":5618,"ariaHidden":602},[601],[572,5620,5622,5625,5628,5631],{"className":5621},[606],[572,5623],{"className":5624,"style":784},[610],[572,5626,1354],{"className":5627,"style":1385},[1094,1383,1384],[572,5629],{"className":5630,"style":1098},[748],[572,5632,5634,5637,5722],{"className":5633},[615],[572,5635],{"className":5636},[791,792],[572,5638,5640],{"className":5639},[654],[572,5641,5643,5714],{"className":5642},[702,703],[572,5644,5646,5711],{"className":5645},[707],[572,5647,5649,5689,5697],{"className":5648,"style":805},[711],[572,5650,5651,5654],{"style":808},[572,5652],{"className":5653,"style":812},[719],[572,5655,5657],{"className":5656},[724,725,726,727],[572,5658,5660],{"className":5659},[615,727],[572,5661,5663,5666],{"className":5662},[615,727],[572,5664,1364],{"className":5665,"style":1424},[615,693,727],[572,5667,5669],{"className":5668},[698],[572,5670,5672],{"className":5671},[702],[572,5673,5675],{"className":5674},[707],[572,5676,5678],{"className":5677,"style":1647},[711],[572,5679,5680,5683],{"style":1440},[572,5681],{"className":5682,"style":1444},[719],[572,5684,5686],{"className":5685},[724,1448,1449,727],[572,5687,660],{"className":5688},[615,727],[572,5690,5691,5694],{"style":824},[572,5692],{"className":5693,"style":812},[719],[572,5695],{"className":5696,"style":832},[831],[572,5698,5699,5702],{"style":835},[572,5700],{"className":5701,"style":812},[719],[572,5703,5705],{"className":5704},[724,725,726,727],[572,5706,5708],{"className":5707},[615,727],[572,5709,649],{"className":5710},[615,727],[572,5712,735],{"className":5713},[734],[572,5715,5717],{"className":5716},[707],[572,5718,5720],{"className":5719,"style":857},[711],[572,5721],{},[572,5723],{"className":5724},[863,792]," verwechseln, die konvergiert.",[1338,5727,5728,5729,5757],{},"Das Quotientenkriterium für einen Divergenzbeweis halten: Der Grenzwert ",[572,5730,5732,5745],{"className":5731},[575],[572,5733,5735],{"className":5734},[579],[581,5736,5737],{"xmlns":583},[585,5738,5739,5743],{},[588,5740,5741],{},[591,5742,649],{},[595,5744,649],{"encoding":597},[572,5746,5748],{"className":5747,"ariaHidden":602},[601],[572,5749,5751,5754],{"className":5750},[606],[572,5752],{"className":5753,"style":611},[610],[572,5755,649],{"className":5756},[615]," entscheidet nichts.",{"title":5759,"searchDepth":5760,"depth":5760,"links":5761},"",2,[5762,5763,5764,5765],{"id":560,"depth":5760,"text":561},{"id":2124,"depth":5760,"text":2125},{"id":4459,"depth":5760,"text":4460},{"id":5455,"depth":5760,"text":5456},[5767,5770,5773,5776,5779,5782,5785,5788,5790],{"lhs":5768,"rhs":5769},"sum(1 .\u002F (1:4))","25\u002F12",{"lhs":5771,"rhs":5772},"sum(1 .\u002F (1:8))","761\u002F280",{"lhs":5774,"rhs":5775},"round(761\u002F280, 4)","2.7179",{"lhs":5777,"rhs":5778},"round(sum(1 .\u002F (1:10)), 4)","2.929",{"lhs":5780,"rhs":5781},"1 + 3\u002F2","2.5",{"lhs":5783,"rhs":5784},"2^m * 1\u002F2^(m + 1)","1\u002F2",{"lhs":5786,"rhs":5787},"round(sum(1 .\u002F (1:1000)), 3)","7.485",{"lhs":5789,"rhs":5787},"round(log(1000) + 0.5772, 3)",{"lhs":5791,"rhs":5792},"round(exp(20 - 0.5772)\u002F10^8, 1)","2.7",null,"md","harmonic-series","\\sum_{k=1}^{\\infty} \\frac{1}{k} = 1 + \\frac{1}{2} + \\frac{1}{3} + \\frac{1}{4} + \\ldots = \\infty","\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>k\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmunderover>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>+\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo>+\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo>+\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmn>4\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo>+\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\sum_{k=1}^{\\infty} \\frac{1}{k} = 1 + \\frac{1}{2} + \\frac{1}{3} + \\frac{1}{4} + \\ldots = \\infty\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" 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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:1.3021em;\">\u003Cspan>\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=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\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:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\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:0.7278em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\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:2.0074em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\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:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" 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class=\"mord\">1\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:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\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:2.0074em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">4\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\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:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\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:0.3669em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">…\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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fharmonische-reihe",[],[5804,5805,5806],"leibniz-criterion","geometric-series","ratio-test",{"title":548,"description":5759},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fharmonische-reihe","Die harmonische Reihe 1 + 1\u002F2 + 1\u002F3 + … divergiert, obwohl ihre Glieder gegen 0 gehen.",[5811,5812,5813,5814],"reihe","divergenz","harmonische zahlen","nullfolge",[5816],{"symbol":1364,"meaning":5817,"symbolHtml":5818},"Summationsindex, durchläuft die natürlichen Zahlen ab 1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k\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:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","3UJCwJMgToeNmFr0C9X_yOR0CyJ4tdx3E6TUxNSG2dU",[5821,5824,5827],{"stem":5822,"title":5823,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fleibniz-kriterium","Leibniz-Kriterium",{"stem":5825,"title":5826,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fquotientenkriterium","Quotientenkriterium",{"stem":5828,"title":5829,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Funendliche-geometrische-reihe","Unendliche geometrische Reihe",1793824264068]