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\\frac{\\pi^2}{6}",[569,978,980,1007],{"className":979,"ariaHidden":616},[615],[569,981,983,986,989,992,995,998,1001,1004],{"className":982},[620],[569,984],{"className":985,"style":921},[624],[569,987,899],{"className":988,"style":925},[641,688],[569,990,903],{"className":991},[645],[569,993,957],{"className":994},[641],[569,996,908],{"className":997},[761],[569,999],{"className":1000,"style":806},[636],[569,1002,784],{"className":1003},[810],[569,1005],{"className":1006,"style":806},[636],[569,1008,1010,1014],{"className":1009},[620],[569,1011],{"className":1012,"style":1013},[624],"height:1.3629em;vertical-align:-0.345em;",[569,1015,1017,1020,1109],{"className":1016},[641],[569,1018],{"className":1019},[645,646],[569,1021,1023],{"className":1022},[592],[569,1024,1026,1101],{"className":1025},[653,654],[569,1027,1029,1098],{"className":1028},[658],[569,1030,1033,1047,1055],{"className":1031,"style":1032},[662],"height:1.0179em;",[569,1034,1035,1038],{"style":666},[569,1036],{"className":1037,"style":671},[670],[569,1039,1041],{"className":1040},[675,676,677,678],[569,1042,1044],{"className":1043},[641,678],[569,1045,973],{"className":1046},[641,678],[569,1048,1049,1052],{"style":720},[569,1050],{"className":1051,"style":671},[670],[569,1053],{"className":1054,"style":728},[727],[569,1056,1057,1060],{"style":731},[569,1058],{"className":1059,"style":671},[670],[569,1061,1063],{"className":1062},[675,676,677,678],[569,1064,1066],{"className":1065},[641,678],[569,1067,1069,1073],{"className":1068},[641,678],[569,1070,968],{"className":1071,"style":1072},[641,688,678],"margin-right:0.0359em;",[569,1074,1076],{"className":1075},[692],[569,1077,1079],{"className":1078},[653],[569,1080,1082],{"className":1081},[658],[569,1083,1086],{"className":1084,"style":1085},[662],"height:0.8913em;",[569,1087,1089,1092],{"style":1088},"top:-2.931em;margin-right:0.0714em;",[569,1090],{"className":1091,"style":709},[670],[569,1093,1095],{"className":1094},[675,713,714,678],[569,1096,957],{"className":1097},[641,678],[569,1099,748],{"className":1100},[747],[569,1102,1104],{"className":1103},[658],[569,1105,1107],{"className":1106,"style":755},[662],[569,1108],{},[569,1110],{"className":1111},[761,646]," und ",[569,1114,1116,1150],{"className":1115},[572],[569,1117,1119],{"className":1118},[576],[578,1120,1121],{"xmlns":580},[582,1122,1123,1147],{},[585,1124,1125,1127,1129,1132,1134,1136],{},[602,1126,899],{},[588,1128,903],{"stretchy":902},[595,1130,1131],{},"4",[588,1133,908],{"stretchy":902},[588,1135,784],{},[592,1137,1138,1144],{},[599,1139,1140,1142],{},[602,1141,968],{},[595,1143,1131],{},[595,1145,1146],{},"90",[608,1148,1149],{"encoding":610},"\\zeta(4) = \\frac{\\pi^4}{90}",[569,1151,1153,1180],{"className":1152,"ariaHidden":616},[615],[569,1154,1156,1159,1162,1165,1168,1171,1174,1177],{"className":1155},[620],[569,1157],{"className":1158,"style":921},[624],[569,1160,899],{"className":1161,"style":925},[641,688],[569,1163,903],{"className":1164},[645],[569,1166,1131],{"className":1167},[641],[569,1169,908],{"className":1170},[761],[569,1172],{"className":1173,"style":806},[636],[569,1175,784],{"className":1176},[810],[569,1178],{"className":1179,"style":806},[636],[569,1181,1183,1186],{"className":1182},[620],[569,1184],{"className":1185,"style":1013},[624],[569,1187,1189,1192,1277],{"className":1188},[641],[569,1190],{"className":1191},[645,646],[569,1193,1195],{"className":1194},[592],[569,1196,1198,1269],{"className":1197},[653,654],[569,1199,1201,1266],{"className":1200},[658],[569,1202,1204,1218,1226],{"className":1203,"style":1032},[662],[569,1205,1206,1209],{"style":666},[569,1207],{"className":1208,"style":671},[670],[569,1210,1212],{"className":1211},[675,676,677,678],[569,1213,1215],{"className":1214},[641,678],[569,1216,1146],{"className":1217},[641,678],[569,1219,1220,1223],{"style":720},[569,1221],{"className":1222,"style":671},[670],[569,1224],{"className":1225,"style":728},[727],[569,1227,1228,1231],{"style":731},[569,1229],{"className":1230,"style":671},[670],[569,1232,1234],{"className":1233},[675,676,677,678],[569,1235,1237],{"className":1236},[641,678],[569,1238,1240,1243],{"className":1239},[641,678],[569,1241,968],{"className":1242,"style":1072},[641,688,678],[569,1244,1246],{"className":1245},[692],[569,1247,1249],{"className":1248},[653],[569,1250,1252],{"className":1251},[658],[569,1253,1255],{"className":1254,"style":1085},[662],[569,1256,1257,1260],{"style":1088},[569,1258],{"className":1259,"style":709},[670],[569,1261,1263],{"className":1262},[675,713,714,678],[569,1264,1131],{"className":1265},[641,678],[569,1267,748],{"className":1268},[747],[569,1270,1272],{"className":1271},[658],[569,1273,1275],{"className":1274,"style":755},[662],[569,1276],{},[569,1278],{"className":1279},[761,646],".",[829,1282,1283,1333,1334,1337],{},[569,1284,1286,1303],{"className":1285},[572],[569,1287,1289],{"className":1288},[576],[578,1290,1291],{"xmlns":580},[582,1292,1293,1301],{},[585,1294,1295,1297,1299],{},[602,1296,565],{},[588,1298,784],{},[595,1300,597],{},[608,1302,789],{"encoding":610},[569,1304,1306,1324],{"className":1305,"ariaHidden":616},[615],[569,1307,1309,1312,1315,1318,1321],{"className":1308},[620],[569,1310],{"className":1311,"style":799},[624],[569,1313,565],{"className":1314},[641,688],[569,1316],{"className":1317,"style":806},[636],[569,1319,784],{"className":1320},[810],[569,1322],{"className":1323,"style":806},[636],[569,1325,1327,1330],{"className":1326},[620],[569,1328],{"className":1329,"style":820},[624],[569,1331,597],{"className":1332},[641],": Die ",[764,1335,1336],{},"harmonische Reihe",", sie divergiert.",[829,1339,1340,1392,1393,1491,1492,1546],{},[569,1341,1343,1362],{"className":1342},[572],[569,1344,1346],{"className":1345},[576],[578,1347,1348],{"xmlns":580},[582,1349,1350,1359],{},[585,1351,1352,1354,1357],{},[602,1353,565],{},[588,1355,1356],{},"\u003C",[595,1358,597],{},[608,1360,1361],{"encoding":610},"p \u003C 1",[569,1363,1365,1383],{"className":1364,"ariaHidden":616},[615],[569,1366,1368,1371,1374,1377,1380],{"className":1367},[620],[569,1369],{"className":1370,"style":862},[624],[569,1372,565],{"className":1373},[641,688],[569,1375],{"className":1376,"style":806},[636],[569,1378,1356],{"className":1379},[810],[569,1381],{"className":1382,"style":806},[636],[569,1384,1386,1389],{"className":1385},[620],[569,1387],{"className":1388,"style":820},[624],[569,1390,597],{"className":1391},[641],": Die Glieder sind größer als ",[569,1394,1396,1414],{"className":1395},[572],[569,1397,1399],{"className":1398},[576],[578,1400,1401],{"xmlns":580},[582,1402,1403,1411],{},[585,1404,1405],{},[592,1406,1407,1409],{},[595,1408,597],{},[602,1410,604],{},[608,1412,1413],{"encoding":610},"\\frac{1}{n}",[569,1415,1417],{"className":1416,"ariaHidden":616},[615],[569,1418,1420,1423],{"className":1419},[620],[569,1421],{"className":1422,"style":625},[624],[569,1424,1426,1429,1488],{"className":1425},[641],[569,1427],{"className":1428},[645,646],[569,1430,1432],{"className":1431},[592],[569,1433,1435,1480],{"className":1434},[653,654],[569,1436,1438,1477],{"className":1437},[658],[569,1439,1441,1455,1463],{"className":1440,"style":663},[662],[569,1442,1443,1446],{"style":666},[569,1444],{"className":1445,"style":671},[670],[569,1447,1449],{"className":1448},[675,676,677,678],[569,1450,1452],{"className":1451},[641,678],[569,1453,604],{"className":1454},[641,688,678],[569,1456,1457,1460],{"style":720},[569,1458],{"className":1459,"style":671},[670],[569,1461],{"className":1462,"style":728},[727],[569,1464,1465,1468],{"style":731},[569,1466],{"className":1467,"style":671},[670],[569,1469,1471],{"className":1470},[675,676,677,678],[569,1472,1474],{"className":1473},[641,678],[569,1475,597],{"className":1476},[641,678],[569,1478,748],{"className":1479},[747],[569,1481,1483],{"className":1482},[658],[569,1484,1486],{"className":1485,"style":755},[662],[569,1487],{},[569,1489],{"className":1490},[761,646],", die Reihe divergiert erst recht. Für ",[569,1493,1495,1515],{"className":1494},[572],[569,1496,1498],{"className":1497},[576],[578,1499,1500],{"xmlns":580},[582,1501,1502,1512],{},[585,1503,1504,1506,1509],{},[602,1505,565],{},[588,1507,1508],{},"≤",[595,1510,1511],{},"0",[608,1513,1514],{"encoding":610},"p \\leq 0",[569,1516,1518,1537],{"className":1517,"ariaHidden":616},[615],[569,1519,1521,1525,1528,1531,1534],{"className":1520},[620],[569,1522],{"className":1523,"style":1524},[624],"height:0.8304em;vertical-align:-0.1944em;",[569,1526,565],{"className":1527},[641,688],[569,1529],{"className":1530,"style":806},[636],[569,1532,1508],{"className":1533},[810],[569,1535],{"className":1536,"style":806},[636],[569,1538,1540,1543],{"className":1539},[620],[569,1541],{"className":1542,"style":820},[624],[569,1544,1511],{"className":1545},[641]," bilden die Glieder nicht einmal eine Nullfolge.",[565,1548,1549,1550,1553,1554,1648,1649,1976,1977,2032,2033,2108],{},"Der Beweis gelingt mit dem ",[764,1551,1552],{},"Integralkriterium",": Für ",[569,1555,1557,1577],{"className":1556},[572],[569,1558,1560],{"className":1559},[576],[578,1561,1562],{"xmlns":580},[582,1563,1564,1574],{},[585,1565,1566,1568,1572],{},[602,1567,565],{},[588,1569,1571],{"mathvariant":1570},"normal","≠",[595,1573,597],{},[608,1575,1576],{"encoding":610},"p \\neq 1",[569,1578,1580,1639],{"className":1579,"ariaHidden":616},[615],[569,1581,1583,1587,1590,1593,1636],{"className":1582},[620],[569,1584],{"className":1585,"style":1586},[624],"height:0.8889em;vertical-align:-0.1944em;",[569,1588,565],{"className":1589},[641,688],[569,1591],{"className":1592,"style":806},[636],[569,1594,1596,1629,1633],{"className":1595},[810],[569,1597,1599],{"className":1598},[810],[569,1600,1603],{"className":1601},[641,1602],"vbox",[569,1604,1607],{"className":1605},[1606],"thinbox",[569,1608,1611,1614,1625],{"className":1609},[1610],"rlap",[569,1612],{"className":1613,"style":1586},[624],[569,1615,1618],{"className":1616},[1617],"inner",[569,1619,1621],{"className":1620},[641],[569,1622,1624],{"className":1623},[810],"",[569,1626],{"className":1627},[1628],"fix",[569,1630],{"className":1631},[636,1632],"nobreak",[569,1634,784],{"className":1635},[810],[569,1637],{"className":1638,"style":806},[636],[569,1640,1642,1645],{"className":1641},[620],[569,1643],{"className":1644,"style":820},[624],[569,1646,597],{"className":1647},[641]," ist ",[569,1650,1652,1726],{"className":1651},[572],[569,1653,1655],{"className":1654},[576],[578,1656,1657],{"xmlns":580},[582,1658,1659,1723],{},[585,1660,1661,1672,1684,1688,1691,1693,1695],{},[1662,1663,1664,1667,1669],"msubsup",{},[588,1665,1666],{},"∫",[595,1668,597],{},[602,1670,1671],{},"N",[599,1673,1674,1677],{},[602,1675,1676],{},"x",[585,1678,1679,1682],{},[588,1680,1681],{},"−",[602,1683,565],{},[1685,1686,1687],"mtext",{}," ",[602,1689,1690],{},"d",[602,1692,1676],{},[588,1694,784],{},[592,1696,1697,1715],{},[585,1698,1699,1711,1713],{},[599,1700,1701,1703],{},[602,1702,1671],{},[585,1704,1705,1707,1709],{},[595,1706,597],{},[588,1708,1681],{},[602,1710,565],{},[588,1712,1681],{},[595,1714,597],{},[585,1716,1717,1719,1721],{},[595,1718,597],{},[588,1720,1681],{},[602,1722,565],{},[608,1724,1725],{"encoding":610},"\\int_1^N x^{-p}\\,dx = \\frac{N^{1-p} - 1}{1 - p}",[569,1727,1729,1852],{"className":1728,"ariaHidden":616},[615],[569,1730,1732,1736,1794,1797,1834,1837,1840,1843,1846,1849],{"className":1731},[620],[569,1733],{"className":1734,"style":1735},[624],"height:1.3921em;vertical-align:-0.3558em;",[569,1737,1739,1743],{"className":1738},[629],[569,1740,1666],{"className":1741,"style":1742},[629,630,631],"margin-right:0.1945em;position:relative;top:-0.0006em;",[569,1744,1746],{"className":1745},[692],[569,1747,1749,1785],{"className":1748},[653,654],[569,1750,1752,1782],{"className":1751},[658],[569,1753,1756,1769],{"className":1754,"style":1755},[662],"height:1.0362em;",[569,1757,1759,1763],{"style":1758},"top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;",[569,1760],{"className":1761,"style":1762},[670],"height:2.7em;",[569,1764,1766],{"className":1765},[675,676,677,678],[569,1767,597],{"className":1768},[641,678],[569,1770,1772,1775],{"style":1771},"top:-3.2579em;margin-right:0.05em;",[569,1773],{"className":1774,"style":1762},[670],[569,1776,1778],{"className":1777},[675,676,677,678],[569,1779,1671],{"className":1780,"style":1781},[641,688,678],"margin-right:0.109em;",[569,1783,748],{"className":1784},[747],[569,1786,1788],{"className":1787},[658],[569,1789,1792],{"className":1790,"style":1791},[662],"height:0.3558em;",[569,1793],{},[569,1795],{"className":1796,"style":637},[636],[569,1798,1800,1803],{"className":1799},[641],[569,1801,1676],{"className":1802},[641,688],[569,1804,1806],{"className":1805},[692],[569,1807,1809],{"className":1808},[653],[569,1810,1812],{"className":1811},[658],[569,1813,1816],{"className":1814,"style":1815},[662],"height:0.7713em;",[569,1817,1819,1822],{"style":1818},"top:-3.063em;margin-right:0.05em;",[569,1820],{"className":1821,"style":1762},[670],[569,1823,1825],{"className":1824},[675,676,677,678],[569,1826,1828,1831],{"className":1827},[641,678],[569,1829,1681],{"className":1830},[641,678],[569,1832,565],{"className":1833},[641,688,678],[569,1835],{"className":1836,"style":637},[636],[569,1838,1690],{"className":1839},[641,688],[569,1841,1676],{"className":1842},[641,688],[569,1844],{"className":1845,"style":806},[636],[569,1847,784],{"className":1848},[810],[569,1850],{"className":1851,"style":806},[636],[569,1853,1855,1859],{"className":1854},[620],[569,1856],{"className":1857,"style":1858},[624],"height:1.499em;vertical-align:-0.4811em;",[569,1860,1862,1865,1973],{"className":1861},[641],[569,1863],{"className":1864},[645,646],[569,1866,1868],{"className":1867},[592],[569,1869,1871,1964],{"className":1870},[653,654],[569,1872,1874,1961],{"className":1873},[658],[569,1875,1877,1898,1906],{"className":1876,"style":1032},[662],[569,1878,1879,1882],{"style":666},[569,1880],{"className":1881,"style":671},[670],[569,1883,1885],{"className":1884},[675,676,677,678],[569,1886,1888,1891,1895],{"className":1887},[641,678],[569,1889,597],{"className":1890},[641,678],[569,1892,1681],{"className":1893},[1894,678],"mbin",[569,1896,565],{"className":1897},[641,688,678],[569,1899,1900,1903],{"style":720},[569,1901],{"className":1902,"style":671},[670],[569,1904],{"className":1905,"style":728},[727],[569,1907,1908,1911],{"style":731},[569,1909],{"className":1910,"style":671},[670],[569,1912,1914],{"className":1913},[675,676,677,678],[569,1915,1917,1955,1958],{"className":1916},[641,678],[569,1918,1920,1923],{"className":1919},[641,678],[569,1921,1671],{"className":1922,"style":1781},[641,688,678],[569,1924,1926],{"className":1925},[692],[569,1927,1929],{"className":1928},[653],[569,1930,1932],{"className":1931},[658],[569,1933,1935],{"className":1934,"style":1085},[662],[569,1936,1937,1940],{"style":1088},[569,1938],{"className":1939,"style":709},[670],[569,1941,1943],{"className":1942},[675,713,714,678],[569,1944,1946,1949,1952],{"className":1945},[641,678],[569,1947,597],{"className":1948},[641,678],[569,1950,1681],{"className":1951},[1894,678],[569,1953,565],{"className":1954},[641,688,678],[569,1956,1681],{"className":1957},[1894,678],[569,1959,597],{"className":1960},[641,678],[569,1962,748],{"className":1963},[747],[569,1965,1967],{"className":1966},[658],[569,1968,1971],{"className":1969,"style":1970},[662],"height:0.4811em;",[569,1972],{},[569,1974],{"className":1975},[761,646],". Das bleibt für ",[569,1978,1980,2000],{"className":1979},[572],[569,1981,1983],{"className":1982},[576],[578,1984,1985],{"xmlns":580},[582,1986,1987,1997],{},[585,1988,1989,1991,1994],{},[602,1990,1671],{},[588,1992,1993],{},"→",[602,1995,1996],{"mathvariant":1570},"∞",[608,1998,1999],{"encoding":610},"N \\to \\infty",[569,2001,2003,2022],{"className":2002,"ariaHidden":616},[615],[569,2004,2006,2010,2013,2016,2019],{"className":2005},[620],[569,2007],{"className":2008,"style":2009},[624],"height:0.6833em;",[569,2011,1671],{"className":2012,"style":1781},[641,688],[569,2014],{"className":2015,"style":806},[636],[569,2017,1993],{"className":2018},[810],[569,2020],{"className":2021,"style":806},[636],[569,2023,2025,2029],{"className":2024},[620],[569,2026],{"className":2027,"style":2028},[624],"height:0.4306em;",[569,2030,1996],{"className":2031},[641]," genau dann beschränkt, wenn ",[569,2034,2036,2058],{"className":2035},[572],[569,2037,2039],{"className":2038},[576],[578,2040,2041],{"xmlns":580},[582,2042,2043,2055],{},[585,2044,2045,2047,2049,2051,2053],{},[595,2046,597],{},[588,2048,1681],{},[602,2050,565],{},[588,2052,1356],{},[595,2054,1511],{},[608,2056,2057],{"encoding":610},"1 - p \u003C 0",[569,2059,2061,2081,2099],{"className":2060,"ariaHidden":616},[615],[569,2062,2064,2068,2071,2075,2078],{"className":2063},[620],[569,2065],{"className":2066,"style":2067},[624],"height:0.7278em;vertical-align:-0.0833em;",[569,2069,597],{"className":2070},[641],[569,2072],{"className":2073,"style":2074},[636],"margin-right:0.2222em;",[569,2076,1681],{"className":2077},[1894],[569,2079],{"className":2080,"style":2074},[636],[569,2082,2084,2087,2090,2093,2096],{"className":2083},[620],[569,2085],{"className":2086,"style":862},[624],[569,2088,565],{"className":2089},[641,688],[569,2091],{"className":2092,"style":806},[636],[569,2094,1356],{"className":2095},[810],[569,2097],{"className":2098,"style":806},[636],[569,2100,2102,2105],{"className":2101},[620],[569,2103],{"className":2104,"style":820},[624],[569,2106,1511],{"className":2107},[641]," ist.",[565,2110,2111,2112,2162,2163,2191,2192,1280],{},"Für 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",[569,2164,2166,2179],{"className":2165},[572],[569,2167,2169],{"className":2168},[576],[578,2170,2171],{"xmlns":580},[582,2172,2173,2177],{},[585,2174,2175],{},[602,2176,1671],{},[608,2178,1671],{"encoding":610},[569,2180,2182],{"className":2181,"ariaHidden":616},[615],[569,2183,2185,2188],{"className":2184},[620],[569,2186],{"className":2187,"style":2009},[624],[569,2189,1671],{"className":2190,"style":1781},[641,688]," Gliedern höchstens ",[569,2193,2195,2229],{"className":2194},[572],[569,2196,2198],{"className":2197},[576],[578,2199,2200],{"xmlns":580},[582,2201,2202,2226],{},[585,2203,2204],{},[592,2205,2206,2218],{},[599,2207,2208,2210],{},[602,2209,1671],{},[585,2211,2212,2214,2216],{},[595,2213,597],{},[588,2215,1681],{},[602,2217,565],{},[585,2219,2220,2222,2224],{},[602,2221,565],{},[588,2223,1681],{},[595,2225,597],{},[608,2227,2228],{"encoding":610},"\\frac{N^{1-p}}{p - 1}",[569,2230,2232],{"className":2231,"ariaHidden":616},[615],[569,2233,2235,2238],{"className":2234},[620],[569,2236],{"className":2237,"style":1858},[624],[569,2239,2241,2244,2344],{"className":2240},[641],[569,2242],{"className":2243},[645,646],[569,2245,2247],{"className":2246},[592],[569,2248,2250,2336],{"className":2249},[653,654],[569,2251,2253,2333],{"className":2252},[658],[569,2254,2256,2276,2284],{"className":2255,"style":1032},[662],[569,2257,2258,2261],{"style":666},[569,2259],{"className":2260,"style":671},[670],[569,2262,2264],{"className":2263},[675,676,677,678],[569,2265,2267,2270,2273],{"className":2266},[641,678],[569,2268,565],{"className":2269},[641,688,678],[569,2271,1681],{"className":2272},[1894,678],[569,2274,597],{"className":2275},[641,678],[569,2277,2278,2281],{"style":720},[569,2279],{"className":2280,"style":671},[670],[569,2282],{"className":2283,"style":728},[727],[569,2285,2286,2289],{"style":731},[569,2287],{"className":2288,"style":671},[670],[569,2290,2292],{"className":2291},[675,676,677,678],[569,2293,2295],{"className":2294},[641,678],[569,2296,2298,2301],{"className":2297},[641,678],[569,2299,1671],{"className":2300,"style":1781},[641,688,678],[569,2302,2304],{"className":2303},[692],[569,2305,2307],{"className":2306},[653],[569,2308,2310],{"className":2309},[658],[569,2311,2313],{"className":2312,"style":1085},[662],[569,2314,2315,2318],{"style":1088},[569,2316],{"className":2317,"style":709},[670],[569,2319,2321],{"className":2320},[675,713,714,678],[569,2322,2324,2327,2330],{"className":2323},[641,678],[569,2325,597],{"className":2326},[641,678],[569,2328,1681],{"className":2329},[1894,678],[569,2331,565],{"className":2332},[641,688,678],[569,2334,748],{"className":2335},[747],[569,2337,2339],{"className":2338},[658],[569,2340,2342],{"className":2341,"style":1970},[662],[569,2343],{},[569,2345],{"className":2346},[761,646],[565,2348,2349,2350,2378,2379,1280],{},"Quotienten- und Wurzelkriterium versagen bei diesen Reihen: Der Grenzwert ist für jedes ",[569,2351,2353,2366],{"className":2352},[572],[569,2354,2356],{"className":2355},[576],[578,2357,2358],{"xmlns":580},[582,2359,2360,2364],{},[585,2361,2362],{},[602,2363,565],{},[608,2365,565],{"encoding":610},[569,2367,2369],{"className":2368,"ariaHidden":616},[615],[569,2370,2372,2375],{"className":2371},[620],[569,2373],{"className":2374,"style":799},[624],[569,2376,565],{"className":2377},[641,688]," gleich 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",[569,2496,2498,2513],{"className":2497},[572],[569,2499,2501],{"className":2500},[576],[578,2502,2503],{"xmlns":580},[582,2504,2505,2510],{},[585,2506,2507],{},[595,2508,2509],{},"1,6439",[608,2511,2512],{"encoding":610},"1{,}6439",[569,2514,2516],{"className":2515,"ariaHidden":616},[615],[569,2517,2519,2523,2526,2534],{"className":2518},[620],[569,2520],{"className":2521,"style":2522},[624],"height:0.8389em;vertical-align:-0.1944em;",[569,2524,597],{"className":2525},[641],[569,2527,2529],{"className":2528},[641],[569,2530,2533],{"className":2531},[2532],"mpunct",",",[569,2535,2537],{"className":2536},[641],"6439",", der Grenzwert 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1{,}6449",[569,2571,2573,2682],{"className":2572,"ariaHidden":616},[615],[569,2574,2576,2579,2673,2676,2679],{"className":2575},[620],[569,2577],{"className":2578,"style":1013},[624],[569,2580,2582,2585,2670],{"className":2581},[641],[569,2583],{"className":2584},[645,646],[569,2586,2588],{"className":2587},[592],[569,2589,2591,2662],{"className":2590},[653,654],[569,2592,2594,2659],{"className":2593},[658],[569,2595,2597,2611,2619],{"className":2596,"style":1032},[662],[569,2598,2599,2602],{"style":666},[569,2600],{"className":2601,"style":671},[670],[569,2603,2605],{"className":2604},[675,676,677,678],[569,2606,2608],{"className":2607},[641,678],[569,2609,973],{"className":2610},[641,678],[569,2612,2613,2616],{"style":720},[569,2614],{"className":2615,"style":671},[670],[569,2617],{"className":2618,"style":728},[727],[569,2620,2621,2624],{"style":731},[569,2622],{"className":2623,"style":671},[670],[569,2625,2627],{"className":2626},[675,676,677,678],[569,2628,2630],{"className":2629},[641,678],[569,2631,2633,2636],{"className":2632},[641,678],[569,2634,968],{"className":2635,"style":1072},[641,688,678],[569,2637,2639],{"className":2638},[692],[569,2640,2642],{"className":2641},[653],[569,2643,2645],{"className":2644},[658],[569,2646,2648],{"className":2647,"style":1085},[662],[569,2649,2650,2653],{"style":1088},[569,2651],{"className":2652,"style":709},[670],[569,2654,2656],{"className":2655},[675,713,714,678],[569,2657,957],{"className":2658},[641,678],[569,2660,748],{"className":2661},[747],[569,2663,2665],{"className":2664},[658],[569,2666,2668],{"className":2667,"style":755},[662],[569,2669],{},[569,2671],{"className":2672},[761,646],[569,2674],{"className":2675,"style":806},[636],[569,2677,2563],{"className":2678},[810],[569,2680],{"className":2681,"style":806},[636],[569,2683,2685,2688,2691,2697],{"className":2684},[620],[569,2686],{"className":2687,"style":2522},[624],[569,2689,597],{"className":2690},[641],[569,2692,2694],{"className":2693},[641],[569,2695,2533],{"className":2696},[2532],[569,2698,2700],{"className":2699},[641],"6449",". Der Rest ist höchstens 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\\frac{1}{\\sqrt{n}}",[569,2950,2952],{"className":2951,"ariaHidden":616},[615],[569,2953,2955,2959,2962,2965],{"className":2954},[620],[569,2956],{"className":2957,"style":2958},[624],"height:1.3831em;vertical-align:-0.538em;",[569,2960,590],{"className":2961,"style":632},[629,630,631],[569,2963],{"className":2964,"style":637},[636],[569,2966,2968,2971,3093],{"className":2967},[641],[569,2969],{"className":2970},[645,646],[569,2972,2974],{"className":2973},[592],[569,2975,2977,3084],{"className":2976},[653,654],[569,2978,2980,3081],{"className":2979},[658],[569,2981,2983,3059,3067],{"className":2982,"style":663},[662],[569,2984,2986,2989],{"style":2985},"top:-2.6259em;",[569,2987],{"className":2988,"style":671},[670],[569,2990,2992],{"className":2991},[675,676,677,678],[569,2993,2995],{"className":2994},[641,678],[569,2996,2999],{"className":2997},[641,2998,678],"sqrt",[569,3000,3002,3050],{"className":3001},[653,654],[569,3003,3005,3047],{"className":3004},[658],[569,3006,3009,3024],{"className":3007,"style":3008},[662],"height:0.8059em;",[569,3010,3014,3017],{"className":3011,"style":3013},[3012],"svg-align","top:-3em;",[569,3015],{"className":3016,"style":671},[670],[569,3018,3021],{"className":3019,"style":3020},[641,678],"padding-left:0.833em;",[569,3022,604],{"className":3023},[641,688,678],[569,3025,3027,3030],{"style":3026},"top:-2.7659em;",[569,3028],{"className":3029,"style":671},[670],[569,3031,3035],{"className":3032,"style":3034},[3033,678],"hide-tail","min-width:0.853em;height:1.08em;",[3036,3037,3043],"svg",{"xmlns":3038,"width":3039,"height":3040,"viewBox":3041,"preserveAspectRatio":3042},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[3044,3045],"path",{"d":3046},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[569,3048,748],{"className":3049},[747],[569,3051,3053],{"className":3052},[658],[569,3054,3057],{"className":3055,"style":3056},[662],"height:0.2341em;",[569,3058],{},[569,3060,3061,3064],{"style":720},[569,3062],{"className":3063,"style":671},[670],[569,3065],{"className":3066,"style":728},[727],[569,3068,3069,3072],{"style":731},[569,3070],{"className":3071,"style":671},[670],[569,3073,3075],{"className":3074},[675,676,677,678],[569,3076,3078],{"className":3077},[641,678],[569,3079,597],{"className":3080},[641,678],[569,3082,748],{"className":3083},[747],[569,3085,3087],{"className":3086},[658],[569,3088,3091],{"className":3089,"style":3090},[662],"height:0.538em;",[569,3092],{},[569,3094],{"className":3095},[761,646]," divergiert. Die Teilsumme bis ",[569,3098,3100,3114],{"className":3099},[572],[569,3101,3103],{"className":3102},[576],[578,3104,3105],{"xmlns":580},[582,3106,3107,3112],{},[585,3108,3109],{},[595,3110,3111],{},"100",[608,3113,3111],{"encoding":610},[569,3115,3117],{"className":3116,"ariaHidden":616},[615],[569,3118,3120,3123],{"className":3119},[620],[569,3121],{"className":3122,"style":820},[624],[569,3124,3111],{"className":3125},[641]," ist schon etwa ",[569,3128,3130,3145],{"className":3129},[572],[569,3131,3133],{"className":3132},[576],[578,3134,3135],{"xmlns":580},[582,3136,3137,3142],{},[585,3138,3139],{},[595,3140,3141],{},"18,59",[608,3143,3144],{"encoding":610},"18{,}59",[569,3146,3148],{"className":3147,"ariaHidden":616},[615],[569,3149,3151,3154,3158,3164],{"className":3150},[620],[569,3152],{"className":3153,"style":2522},[624],[569,3155,3157],{"className":3156},[641],"18",[569,3159,3161],{"className":3160},[641],[569,3162,2533],{"className":3163},[2532],[569,3165,3167],{"className":3166},[641],"59",[565,3169,3170,3232,3233,2494,3261,3302,3303,3497,3498,3551,3552,1280],{},[569,3171,3173,3192],{"className":3172},[572],[569,3174,3176],{"className":3175},[576],[578,3177,3178],{"xmlns":580},[582,3179,3180,3189],{},[585,3181,3182,3184,3186],{},[602,3183,565],{},[588,3185,784],{},[595,3187,3188],{},"1,01",[608,3190,3191],{"encoding":610},"p = 1{,}01",[569,3193,3195,3213],{"className":3194,"ariaHidden":616},[615],[569,3196,3198,3201,3204,3207,3210],{"className":3197},[620],[569,3199],{"className":3200,"style":799},[624],[569,3202,565],{"className":3203},[641,688],[569,3205],{"className":3206,"style":806},[636],[569,3208,784],{"className":3209},[810],[569,3211],{"className":3212,"style":806},[636],[569,3214,3216,3219,3222,3228],{"className":3215},[620],[569,3217],{"className":3218,"style":2522},[624],[569,3220,597],{"className":3221},[641],[569,3223,3225],{"className":3224},[641],[569,3226,2533],{"className":3227},[2532],[569,3229,3231],{"className":3230},[641],"01",": Die Reihe konvergiert, aber sehr langsam. Die Teilsumme bis ",[569,3234,3236,3249],{"className":3235},[572],[569,3237,3239],{"className":3238},[576],[578,3240,3241],{"xmlns":580},[582,3242,3243,3247],{},[585,3244,3245],{},[595,3246,2479],{},[608,3248,2479],{"encoding":610},[569,3250,3252],{"className":3251,"ariaHidden":616},[615],[569,3253,3255,3258],{"className":3254},[620],[569,3256],{"className":3257,"style":820},[624],[569,3259,2479],{"className":3260},[641],[569,3262,3264,3279],{"className":3263},[572],[569,3265,3267],{"className":3266},[576],[578,3268,3269],{"xmlns":580},[582,3270,3271,3276],{},[585,3272,3273],{},[595,3274,3275],{},"7,25",[608,3277,3278],{"encoding":610},"7{,}25",[569,3280,3282],{"className":3281,"ariaHidden":616},[615],[569,3283,3285,3288,3292,3298],{"className":3284},[620],[569,3286],{"className":3287,"style":2522},[624],[569,3289,3291],{"className":3290},[641],"7",[569,3293,3295],{"className":3294},[641],[569,3296,2533],{"className":3297},[2532],[569,3299,3301],{"className":3300},[641],"25",", der Rest danach kann laut Schranke noch bis zu ",[569,3304,3306,3338],{"className":3305},[572],[569,3307,3309],{"className":3308},[576],[578,3310,3311],{"xmlns":580},[582,3312,3313,3335],{},[585,3314,3315,3330,3332],{},[592,3316,3317,3328],{},[599,3318,3319,3321],{},[595,3320,2479],{},[585,3322,3323,3325],{},[588,3324,1681],{},[595,3326,3327],{},"0,01",[595,3329,3327],{},[588,3331,2563],{},[595,3333,3334],{},"93,3",[608,3336,3337],{"encoding":610},"\\frac{1000^{-0{,}01}}{0{,}01} \\approx 93{,}3",[569,3339,3341,3477],{"className":3340,"ariaHidden":616},[615],[569,3342,3344,3347,3468,3471,3474],{"className":3343},[620],[569,3345],{"className":3346,"style":1858},[624],[569,3348,3350,3353,3465],{"className":3349},[641],[569,3351],{"className":3352},[645,646],[569,3354,3356],{"className":3355},[592],[569,3357,3359,3457],{"className":3358},[653,654],[569,3360,3362,3454],{"className":3361},[658],[569,3363,3365,3388,3396],{"className":3364,"style":1032},[662],[569,3366,3367,3370],{"style":666},[569,3368],{"className":3369,"style":671},[670],[569,3371,3373],{"className":3372},[675,676,677,678],[569,3374,3376,3379,3385],{"className":3375},[641,678],[569,3377,1511],{"className":3378},[641,678],[569,3380,3382],{"className":3381},[641,678],[569,3383,2533],{"className":3384},[2532,678],[569,3386,3231],{"className":3387},[641,678],[569,3389,3390,3393],{"style":720},[569,3391],{"className":3392,"style":671},[670],[569,3394],{"className":3395,"style":728},[727],[569,3397,3398,3401],{"style":731},[569,3399],{"className":3400,"style":671},[670],[569,3402,3404],{"className":3403},[675,676,677,678],[569,3405,3407,3410],{"className":3406},[641,678],[569,3408,3111],{"className":3409},[641,678],[569,3411,3413,3416],{"className":3412},[641,678],[569,3414,1511],{"className":3415},[641,678],[569,3417,3419],{"className":3418},[692],[569,3420,3422],{"className":3421},[653],[569,3423,3425],{"className":3424},[658],[569,3426,3428],{"className":3427,"style":1085},[662],[569,3429,3430,3433],{"style":1088},[569,3431],{"className":3432,"style":709},[670],[569,3434,3436],{"className":3435},[675,713,714,678],[569,3437,3439,3442,3445,3451],{"className":3438},[641,678],[569,3440,1681],{"className":3441},[641,678],[569,3443,1511],{"className":3444},[641,678],[569,3446,3448],{"className":3447},[641,678],[569,3449,2533],{"className":3450},[2532,678],[569,3452,3231],{"className":3453},[641,678],[569,3455,748],{"className":3456},[747],[569,3458,3460],{"className":3459},[658],[569,3461,3463],{"className":3462,"style":1970},[662],[569,3464],{},[569,3466],{"className":3467},[761,646],[569,3469],{"className":3470,"style":806},[636],[569,3472,2563],{"className":3473},[810],[569,3475],{"className":3476,"style":806},[636],[569,3478,3480,3483,3487,3493],{"className":3479},[620],[569,3481],{"className":3482,"style":2522},[624],[569,3484,3486],{"className":3485},[641],"93",[569,3488,3490],{"className":3489},[641],[569,3491,2533],{"className":3492},[2532],[569,3494,3496],{"className":3495},[641],"3"," betragen. Der Grenzwert ",[569,3499,3501,3521],{"className":3500},[572],[569,3502,3504],{"className":3503},[576],[578,3505,3506],{"xmlns":580},[582,3507,3508,3518],{},[585,3509,3510,3512,3514,3516],{},[602,3511,899],{},[588,3513,903],{"stretchy":902},[595,3515,3188],{},[588,3517,908],{"stretchy":902},[608,3519,3520],{"encoding":610},"\\zeta(1{,}01)",[569,3522,3524],{"className":3523,"ariaHidden":616},[615],[569,3525,3527,3530,3533,3536,3539,3545,3548],{"className":3526},[620],[569,3528],{"className":3529,"style":921},[624],[569,3531,899],{"className":3532,"style":925},[641,688],[569,3534,903],{"className":3535},[645],[569,3537,597],{"className":3538},[641],[569,3540,3542],{"className":3541},[641],[569,3543,2533],{"className":3544},[2532],[569,3546,3231],{"className":3547},[641],[569,3549,908],{"className":3550},[761]," liegt bei etwa ",[569,3553,3555,3570],{"className":3554},[572],[569,3556,3558],{"className":3557},[576],[578,3559,3560],{"xmlns":580},[582,3561,3562,3567],{},[585,3563,3564],{},[595,3565,3566],{},"100,6",[608,3568,3569],{"encoding":610},"100{,}6",[569,3571,3573],{"className":3572,"ariaHidden":616},[615],[569,3574,3576,3579,3582,3588],{"className":3575},[620],[569,3577],{"className":3578,"style":2522},[624],[569,3580,3111],{"className":3581},[641],[569,3583,3585],{"className":3584},[641],[569,3586,2533],{"className":3587},[2532],[569,3589,973],{"className":3590},[641],[560,3592,3594],{"id":3593},"typische-fehler","Typische Fehler",[826,3596,3597,3855,3970],{},[829,3598,3599,3600,3750,3751,3825,3826,3854],{},"Aus ",[569,3601,3603,3629],{"className":3602},[572],[569,3604,3606],{"className":3605},[576],[578,3607,3608],{"xmlns":580},[582,3609,3610,3626],{},[585,3611,3612,3622,3624],{},[592,3613,3614,3616],{},[595,3615,597],{},[599,3617,3618,3620],{},[602,3619,604],{},[602,3621,565],{},[588,3623,1993],{},[595,3625,1511],{},[608,3627,3628],{"encoding":610},"\\frac{1}{n^p} \\to 0",[569,3630,3632,3741],{"className":3631,"ariaHidden":616},[615],[569,3633,3635,3638,3732,3735,3738],{"className":3634},[620],[569,3636],{"className":3637,"style":625},[624],[569,3639,3641,3644,3729],{"className":3640},[641],[569,3642],{"className":3643},[645,646],[569,3645,3647],{"className":3646},[592],[569,3648,3650,3721],{"className":3649},[653,654],[569,3651,3653,3718],{"className":3652},[658],[569,3654,3656,3696,3704],{"className":3655,"style":663},[662],[569,3657,3658,3661],{"style":666},[569,3659],{"className":3660,"style":671},[670],[569,3662,3664],{"className":3663},[675,676,677,678],[569,3665,3667],{"className":3666},[641,678],[569,3668,3670,3673],{"className":3669},[641,678],[569,3671,604],{"className":3672},[641,688,678],[569,3674,3676],{"className":3675},[692],[569,3677,3679],{"className":3678},[653],[569,3680,3682],{"className":3681},[658],[569,3683,3685],{"className":3684,"style":702},[662],[569,3686,3687,3690],{"style":705},[569,3688],{"className":3689,"style":709},[670],[569,3691,3693],{"className":3692},[675,713,714,678],[569,3694,565],{"className":3695},[641,688,678],[569,3697,3698,3701],{"style":720},[569,3699],{"className":3700,"style":671},[670],[569,3702],{"className":3703,"style":728},[727],[569,3705,3706,3709],{"style":731},[569,3707],{"className":3708,"style":671},[670],[569,3710,3712],{"className":3711},[675,676,677,678],[569,3713,3715],{"className":3714},[641,678],[569,3716,597],{"className":3717},[641,678],[569,3719,748],{"className":3720},[747],[569,3722,3724],{"className":3723},[658],[569,3725,3727],{"className":3726,"style":755},[662],[569,3728],{},[569,3730],{"className":3731},[761,646],[569,3733],{"className":3734,"style":806},[636],[569,3736,1993],{"className":3737},[810],[569,3739],{"className":3740,"style":806},[636],[569,3742,3744,3747],{"className":3743},[620],[569,3745],{"className":3746,"style":820},[624],[569,3748,1511],{"className":3749},[641]," auf Konvergenz schließen. Für ",[569,3752,3754,3776],{"className":3753},[572],[569,3755,3757],{"className":3756},[576],[578,3758,3759],{"xmlns":580},[582,3760,3761,3773],{},[585,3762,3763,3765,3767,3769,3771],{},[595,3764,1511],{},[588,3766,1356],{},[602,3768,565],{},[588,3770,1508],{},[595,3772,597],{},[608,3774,3775],{"encoding":610},"0 \u003C p \\leq 1",[569,3777,3779,3798,3816],{"className":3778,"ariaHidden":616},[615],[569,3780,3782,3786,3789,3792,3795],{"className":3781},[620],[569,3783],{"className":3784,"style":3785},[624],"height:0.6835em;vertical-align:-0.0391em;",[569,3787,1511],{"className":3788},[641],[569,3790],{"className":3791,"style":806},[636],[569,3793,1356],{"className":3794},[810],[569,3796],{"className":3797,"style":806},[636],[569,3799,3801,3804,3807,3810,3813],{"className":3800},[620],[569,3802],{"className":3803,"style":1524},[624],[569,3805,565],{"className":3806},[641,688],[569,3808],{"className":3809,"style":806},[636],[569,3811,1508],{"className":3812},[810],[569,3814],{"className":3815,"style":806},[636],[569,3817,3819,3822],{"className":3818},[620],[569,3820],{"className":3821,"style":820},[624],[569,3823,597],{"className":3824},[641]," gehen die Glieder gegen ",[569,3827,3829,3842],{"className":3828},[572],[569,3830,3832],{"className":3831},[576],[578,3833,3834],{"xmlns":580},[582,3835,3836,3840],{},[585,3837,3838],{},[595,3839,1511],{},[608,3841,1511],{"encoding":610},[569,3843,3845],{"className":3844,"ariaHidden":616},[615],[569,3846,3848,3851],{"className":3847},[620],[569,3849],{"className":3850,"style":820},[624],[569,3852,1511],{"className":3853},[641],", die Reihe divergiert trotzdem.",[829,3856,3857,3858,3908,3909,3937,3938,3941,3942,1280],{},"Den Grenzfall ",[569,3859,3861,3878],{"className":3860},[572],[569,3862,3864],{"className":3863},[576],[578,3865,3866],{"xmlns":580},[582,3867,3868,3876],{},[585,3869,3870,3872,3874],{},[602,3871,565],{},[588,3873,784],{},[595,3875,597],{},[608,3877,789],{"encoding":610},[569,3879,3881,3899],{"className":3880,"ariaHidden":616},[615],[569,3882,3884,3887,3890,3893,3896],{"className":3883},[620],[569,3885],{"className":3886,"style":799},[624],[569,3888,565],{"className":3889},[641,688],[569,3891],{"className":3892,"style":806},[636],[569,3894,784],{"className":3895},[810],[569,3897],{"className":3898,"style":806},[636],[569,3900,3902,3905],{"className":3901},[620],[569,3903],{"className":3904,"style":820},[624],[569,3906,597],{"className":3907},[641]," der Konvergenz zuschlagen. Konvergenz gilt nur für ",[569,3910,3912,3925],{"className":3911},[572],[569,3913,3915],{"className":3914},[576],[578,3916,3917],{"xmlns":580},[582,3918,3919,3923],{},[585,3920,3921],{},[602,3922,565],{},[608,3924,565],{"encoding":610},[569,3926,3928],{"className":3927,"ariaHidden":616},[615],[569,3929,3931,3934],{"className":3930},[620],[569,3932],{"className":3933,"style":799},[624],[569,3935,565],{"className":3936},[641,688]," ",[764,3939,3940],{},"echt größer"," als ",[569,3943,3945,3958],{"className":3944},[572],[569,3946,3948],{"className":3947},[576],[578,3949,3950],{"xmlns":580},[582,3951,3952,3956],{},[585,3953,3954],{},[595,3955,597],{},[608,3957,597],{"encoding":610},[569,3959,3961],{"className":3960,"ariaHidden":616},[615],[569,3962,3964,3967],{"className":3963},[620],[569,3965],{"className":3966,"style":820},[624],[569,3968,597],{"className":3969},[641],[829,3971,3972,3973,4001],{},"Das Quotientenkriterium versuchen und aus dem Grenzwert ",[569,3974,3976,3989],{"className":3975},[572],[569,3977,3979],{"className":3978},[576],[578,3980,3981],{"xmlns":580},[582,3982,3983,3987],{},[585,3984,3985],{},[595,3986,597],{},[608,3988,597],{"encoding":610},[569,3990,3992],{"className":3991,"ariaHidden":616},[615],[569,3993,3995,3998],{"className":3994},[620],[569,3996],{"className":3997,"style":820},[624],[569,3999,597],{"className":4000},[641]," eine Aussage ableiten.",{"title":4003,"searchDepth":4004,"depth":4004,"links":4005},"",2,[4006,4007,4008],{"id":562,"depth":4004,"text":563},{"id":2409,"depth":4004,"text":2410},{"id":3593,"depth":4004,"text":3594},[4010,4014,4017,4020,4023,4026,4029,4032],{"lhs":4011,"rhs":4012,"where":4013},"round(sum(map(0:999, f(k) = (1 + 2*(k + 0.5)\u002F1000)^(-p)))*2\u002F1000, 4)","round((3^(1 - p) - 1)\u002F(1 - p), 4)",{"p":4004},{"lhs":4015,"rhs":4016},"round(sum(1 .\u002F (1:1000).^2), 4)","1.6439",{"lhs":4018,"rhs":4019},"round(pi^2\u002F6, 4)","1.6449",{"lhs":4021,"rhs":4022},"round(sum(map(1:100, f(n) = 1\u002Fsqrt(n))), 2)","18.59",{"lhs":4024,"rhs":4025},"round(sum(1 .\u002F (1:1000).^1.01), 2)","7.25",{"lhs":4027,"rhs":4028},"round(1000^(-0.01)\u002F0.01, 1)","93.3",{"lhs":4030,"rhs":4031},"round(sum(1 .\u002F (1:1000).^1.01) + 1000.5^(-0.01)\u002F0.01, 1)","100.6",{"lhs":4033,"rhs":4034},"1000^(1 - 2)\u002F(2 - 1)","0.001","p \\in \\mathbb{R}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p \\in \\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:0.7335em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\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>",null,"md","p-series","\\sum_{n=1}^{\\infty} \\frac{1}{n^p} \\text{ konvergiert} \\;\\Leftrightarrow\\; p > 1","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmunderover>\u003Cmo>∑\u003C\u002Fmo>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmunderover>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmsup>\u003Cmi>n\u003C\u002Fmi>\u003Cmi>p\u003C\u002Fmi>\u003C\u002Fmsup>\u003C\u002Fmfrac>\u003Cmtext> konvergiert\u003C\u002Fmtext>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⇔\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmi>p\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\sum_{n=1}^{\\infty} \\frac{1}{n^p} \\text{ konvergiert} \\;\\Leftrightarrow\\; p > 1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.9185em;vertical-align:-1.2671em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.6514em;\">\u003Cspan style=\"top:-1.8829em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">=\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.05em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop op-symbol large-op\">∑\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-4.3em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.2671em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"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\">\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.5904em;\">\u003Cspan style=\"top:-2.989em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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=\"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:0.7335em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fverallgemeinerte-harmonische-reihe",[],[4048,4049,4050,4051],"harmonic-series","integral-test","basel-problem","comparison-test",{"title":548,"description":4003},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fverallgemeinerte-harmonische-reihe","Die Reihe über 1\u002Fnᵖ konvergiert genau für p > 1; für p ≤ 1 divergiert sie, wie die harmonische Reihe.",[4056,4057,4058,4059],"reihe","konvergenz","harmonische reihe","zeta-funktion",[4061,4064],{"symbol":604,"meaning":4062,"symbolHtml":4063},"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":565,"meaning":4065,"symbolHtml":4066},"reeller Exponent","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p\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:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","PAqdGYgAWGAg4czxlVy6KcEugiD5_AqInFFAjG1bZ_o",[4069,4072,4075,4077],{"stem":4070,"title":4071,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fbasler-problem","Summe der reziproken Quadratzahlen",{"stem":4073,"title":4074,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fharmonische-reihe","Harmonische Reihe",{"stem":4076,"title":1552,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fintegralkriterium",{"stem":4078,"title":4079,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fmajorantenkriterium","Majoranten- und Minorantenkriterium",1793824264255]