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1",[572,1079,1081,1140],{"className":1080,"ariaHidden":602},[601],[572,1082,1084,1088,1091,1094,1137],{"className":1083},[606],[572,1085],{"className":1086,"style":1087},[610],"height:0.8889em;vertical-align:-0.1944em;",[572,1089,638],{"className":1090},[615,616],[572,1092],{"className":1093,"style":667},[666],[572,1095,1097,1130,1134],{"className":1096},[671],[572,1098,1100],{"className":1099},[671],[572,1101,1104],{"className":1102},[615,1103],"vbox",[572,1105,1108],{"className":1106},[1107],"thinbox",[572,1109,1112,1115,1126],{"className":1110},[1111],"rlap",[572,1113],{"className":1114,"style":1087},[610],[572,1116,1119],{"className":1117},[1118],"inner",[572,1120,1122],{"className":1121},[615],[572,1123,1125],{"className":1124},[671],"",[572,1127],{"className":1128},[1129],"fix",[572,1131],{"className":1132},[666,1133],"nobreak",[572,1135,792],{"className":1136},[671],[572,1138],{"className":1139,"style":667},[666],[572,1141,1143,1146],{"className":1142},[606],[572,1144],{"className":1145,"style":681},[610],[572,1147,646],{"className":1148},[615],", hat das Wurzelkriterium denselben Grenzwert und entscheidet genauso. Umgekehrt gibt es Reihen, bei denen nur das Wurzelkriterium hilft. Bequem ist es vor allem, wenn ",[572,1151,1153,1171],{"className":1152},[575],[572,1154,1156],{"className":1155},[579],[581,1157,1158],{"xmlns":583},[585,1159,1160,1168],{},[588,1161,1162],{},[861,1163,1164,1166],{},[591,1165,865],{},[591,1167,593],{},[595,1169,1170],{"encoding":597},"a_n",[572,1172,1174],{"className":1173,"ariaHidden":602},[601],[572,1175,1177,1181],{"className":1176},[606],[572,1178],{"className":1179,"style":1180},[610],"height:0.5806em;vertical-align:-0.15em;",[572,1182,1184,1187],{"className":1183},[615],[572,1185,865],{"className":1186},[615,616],[572,1188,1190],{"className":1189},[971],[572,1191,1193,1213],{"className":1192},[904,938],[572,1194,1196,1210],{"className":1195},[908],[572,1197,1199],{"className":1198,"style":981},[912],[572,1200,1201,1204],{"style":984},[572,1202],{"className":1203,"style":988},[920],[572,1205,1207],{"className":1206},[925,926,992,928],[572,1208,593],{"className":1209},[615,616,928],[572,1211,1000],{"className":1212},[999],[572,1214,1216],{"className":1215},[908],[572,1217,1219],{"className":1218,"style":1007},[912],[572,1220],{}," die Form ",[572,1223,1225,1252],{"className":1224},[575],[572,1226,1228],{"className":1227},[579],[581,1229,1230],{"xmlns":583},[585,1231,1232,1249],{},[588,1233,1234,1238,1241],{},[640,1235,1237],{"stretchy":1236},"false","(",[640,1239,1240],{},"…",[1242,1243,1244,1247],"msup",{},[640,1245,1246],{"stretchy":1236},")",[591,1248,593],{},[595,1250,1251],{"encoding":597},"(\\ldots)^n",[572,1253,1255],{"className":1254,"ariaHidden":602},[601],[572,1256,1258,1262,1266,1270],{"className":1257},[606],[572,1259],{"className":1260,"style":1261},[610],"height:1em;vertical-align:-0.25em;",[572,1263,1237],{"className":1264},[1265],"mopen",[572,1267,1240],{"className":1268},[1269],"minner",[572,1271,1274,1277],{"className":1272},[1273],"mclose",[572,1275,1246],{"className":1276},[1273],[572,1278,1280],{"className":1279},[971],[572,1281,1283],{"className":1282},[904],[572,1284,1286],{"className":1285},[908],[572,1287,1290],{"className":1288,"style":1289},[912],"height:0.6644em;",[572,1291,1293,1296],{"style":1292},"top:-3.063em;margin-right:0.05em;",[572,1294],{"className":1295,"style":988},[920],[572,1297,1299],{"className":1298},[925,926,992,928],[572,1300,593],{"className":1301},[615,616,928]," hat. Mit der Formel von Cauchy-Hadamard ",[572,1304,1306,1352],{"className":1305},[575],[572,1307,1309],{"className":1308},[579],[581,1310,1311],{"xmlns":583},[585,1312,1313,1349],{},[588,1314,1315,1318,1320],{},[591,1316,1317],{},"r",[640,1319,792],{},[1321,1322,1323,1325],"mfrac",{},[644,1324,646],{},[588,1326,1327,1330,1332],{},[591,1328,1329],{"mathvariant":858},"lim sup",[640,1331,850],{},[852,1333,1334,1347],{},[588,1335,1336,1338,1345],{},[591,1337,859],{"mathvariant":858},[861,1339,1340,1343],{},[591,1341,1342],{},"c",[591,1344,593],{},[591,1346,859],{"mathvariant":858},[591,1348,593],{},[595,1350,1351],{"encoding":597},"r = \\frac{1}{\\limsup \\sqrt[n]{|c_n|}}",[572,1353,1355,1374],{"className":1354,"ariaHidden":602},[601],[572,1356,1358,1361,1365,1368,1371],{"className":1357},[606],[572,1359],{"className":1360,"style":611},[610],[572,1362,1317],{"className":1363,"style":1364},[615,616],"margin-right:0.0278em;",[572,1366],{"className":1367,"style":667},[666],[572,1369,792],{"className":1370},[671],[572,1372],{"className":1373,"style":667},[666],[572,1375,1377,1381],{"className":1376},[606],[572,1378],{"className":1379,"style":1380},[610],"height:1.6747em;vertical-align:-0.8296em;",[572,1382,1384,1388,1602],{"className":1383},[615],[572,1385],{"className":1386},[1265,1387],"nulldelimiter",[572,1389,1391],{"className":1390},[1321],[572,1392,1394,1593],{"className":1393},[904,938],[572,1395,1397,1590],{"className":1396},[908],[572,1398,1401,1564,1575],{"className":1399,"style":1400},[912],"height:0.8451em;",[572,1402,1404,1408],{"style":1403},"top:-2.4642em;",[572,1405],{"className":1406,"style":1407},[920],"height:3em;",[572,1409,1411],{"className":1410},[925,926,992,928],[572,1412,1414,1429,1432],{"className":1413},[615,928],[572,1415,1417,1421,1425],{"className":1416},[888,928],[572,1418,847],{"className":1419},[615,1420,928],"mathrm",[572,1422],{"className":1423,"style":1424},[666,928],"margin-right:0.1952em;",[572,1426,1428],{"className":1427},[615,1420,928],"sup",[572,1430],{"className":1431,"style":1424},[666,928],[572,1433,1435,1464],{"className":1434},[615,896,928],[572,1436,1438],{"className":1437},[900],[572,1439,1441],{"className":1440},[904],[572,1442,1444],{"className":1443},[908],[572,1445,1448],{"className":1446,"style":1447},[912],"height:0.6779em;",[572,1449,1451,1454],{"style":1450},"top:-2.8704em;",[572,1452],{"className":1453,"style":921},[920],[572,1455,1458],{"className":1456},[925,1457,927,928],"reset-size3",[572,1459,1461],{"className":1460},[615,928],[572,1462,593],{"className":1463},[615,616,928],[572,1465,1467,1555],{"className":1466},[904,938],[572,1468,1470,1552],{"className":1469},[908],[572,1471,1474,1535],{"className":1472,"style":1473},[912],"height:1.0369em;",[572,1475,1478,1482],{"className":1476,"style":1477},[949],"top:-3.4286em;",[572,1479],{"className":1480,"style":1481},[920],"height:3.4286em;",[572,1483,1486,1489,1532],{"className":1484,"style":1485},[615,928],"padding-left:1.19em;",[572,1487,859],{"className":1488},[615,928],[572,1490,1492,1495],{"className":1491},[615,928],[572,1493,1342],{"className":1494},[615,616,928],[572,1496,1498],{"className":1497},[971],[572,1499,1501,1523],{"className":1500},[904,938],[572,1502,1504,1520],{"className":1503},[908],[572,1505,1508],{"className":1506,"style":1507},[912],"height:0.1645em;",[572,1509,1511,1514],{"style":1510},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[572,1512],{"className":1513,"style":921},[920],[572,1515,1517],{"className":1516},[925,1457,927,928],[572,1518,593],{"className":1519},[615,616,928],[572,1521,1000],{"className":1522},[999],[572,1524,1526],{"className":1525},[908],[572,1527,1530],{"className":1528,"style":1529},[912],"height:0.143em;",[572,1531],{},[572,1533,859],{"className":1534},[615,928],[572,1536,1538,1541],{"style":1537},"top:-3.0089em;",[572,1539],{"className":1540,"style":1481},[920],[572,1542,1545],{"className":1543,"style":1544},[1022,928],"min-width:0.853em;height:1.5429em;",[1025,1546,1549],{"xmlns":1027,"width":1028,"height":1547,"viewBox":1548,"preserveAspectRatio":1031},"1.5429em","0 0 400000 1080",[1033,1550],{"d":1551},"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",[572,1553,1000],{"className":1554},[999],[572,1556,1558],{"className":1557},[908],[572,1559,1562],{"className":1560,"style":1561},[912],"height:0.4197em;",[572,1563],{},[572,1565,1567,1570],{"style":1566},"top:-3.23em;",[572,1568],{"className":1569,"style":1407},[920],[572,1571],{"className":1572,"style":1574},[1573],"frac-line","border-bottom-width:0.04em;",[572,1576,1578,1581],{"style":1577},"top:-3.394em;",[572,1579],{"className":1580,"style":1407},[920],[572,1582,1584],{"className":1583},[925,926,992,928],[572,1585,1587],{"className":1586},[615,928],[572,1588,646],{"className":1589},[615,928],[572,1591,1000],{"className":1592},[999],[572,1594,1596],{"className":1595},[908],[572,1597,1600],{"className":1598,"style":1599},[912],"height:0.8296em;",[572,1601],{},[572,1603],{"className":1604},[1273,1387]," bestimmt es den Konvergenzradius einer Potenzreihe ",[572,1607,1609,1637],{"className":1608},[575],[572,1610,1612],{"className":1611},[579],[581,1613,1614],{"xmlns":583},[585,1615,1616,1634],{},[588,1617,1618,1621,1627],{},[640,1619,1620],{},"∑",[861,1622,1623,1625],{},[591,1624,1342],{},[591,1626,593],{},[1242,1628,1629,1632],{},[591,1630,1631],{},"x",[591,1633,593],{},[595,1635,1636],{"encoding":597},"\\sum c_n x^n",[572,1638,1640],{"className":1639,"ariaHidden":602},[601],[572,1641,1643,1646,1652,1655,1695],{"className":1642},[606],[572,1644],{"className":1645,"style":1261},[610],[572,1647,1620],{"className":1648,"style":1651},[888,1649,1650],"op-symbol","small-op","position:relative;top:0em;",[572,1653],{"className":1654,"style":892},[666],[572,1656,1658,1661],{"className":1657},[615],[572,1659,1342],{"className":1660},[615,616],[572,1662,1664],{"className":1663},[971],[572,1665,1667,1687],{"className":1666},[904,938],[572,1668,1670,1684],{"className":1669},[908],[572,1671,1673],{"className":1672,"style":981},[912],[572,1674,1675,1678],{"style":984},[572,1676],{"className":1677,"style":988},[920],[572,1679,1681],{"className":1680},[925,926,992,928],[572,1682,593],{"className":1683},[615,616,928],[572,1685,1000],{"className":1686},[999],[572,1688,1690],{"className":1689},[908],[572,1691,1693],{"className":1692,"style":1007},[912],[572,1694],{},[572,1696,1698,1701],{"className":1697},[615],[572,1699,1631],{"className":1700},[615,616],[572,1702,1704],{"className":1703},[971],[572,1705,1707],{"className":1706},[904],[572,1708,1710],{"className":1709},[908],[572,1711,1713],{"className":1712,"style":1289},[912],[572,1714,1715,1718],{"style":1292},[572,1716],{"className":1717,"style":988},[920],[572,1719,1721],{"className":1720},[925,926,992,928],[572,1722,593],{"className":1723},[615,616,928],[564,1725,1726,1727,1863,1864,2029,2030,689],{},"Nützlich ist der Grenzwert ",[572,1728,1730,1753],{"className":1729},[575],[572,1731,1733],{"className":1732},[579],[581,1734,1735],{"xmlns":583},[585,1736,1737,1750],{},[588,1738,1739,1745,1748],{},[852,1740,1741,1743],{},[591,1742,593],{},[591,1744,593],{},[640,1746,1747],{},"→",[644,1749,646],{},[595,1751,1752],{"encoding":597},"\\sqrt[n]{n} \\to 1",[572,1754,1756,1854],{"className":1755,"ariaHidden":602},[601],[572,1757,1759,1763,1845,1848,1851],{"className":1758},[606],[572,1760],{"className":1761,"style":1762},[610],"height:1.04em;vertical-align:-0.2397em;",[572,1764,1766,1794],{"className":1765},[615,896],[572,1767,1769],{"className":1768},[900],[572,1770,1772],{"className":1771},[904],[572,1773,1775],{"className":1774},[908],[572,1776,1779],{"className":1777,"style":1778},[912],"height:0.5516em;",[572,1780,1782,1785],{"style":1781},"top:-2.8363em;",[572,1783],{"className":1784,"style":921},[920],[572,1786,1788],{"className":1787},[925,926,927,928],[572,1789,1791],{"className":1790},[615,928],[572,1792,593],{"className":1793},[615,616,928],[572,1795,1797,1836],{"className":1796},[904,938],[572,1798,1800,1833],{"className":1799},[908],[572,1801,1804,1818],{"className":1802,"style":1803},[912],"height:0.8003em;",[572,1805,1808,1811],{"className":1806,"style":1807},[949],"top:-3em;",[572,1809],{"className":1810,"style":1407},[920],[572,1812,1815],{"className":1813,"style":1814},[615],"padding-left:0.833em;",[572,1816,593],{"className":1817},[615,616],[572,1819,1821,1824],{"style":1820},"top:-2.7603em;",[572,1822],{"className":1823,"style":1407},[920],[572,1825,1828],{"className":1826,"style":1827},[1022],"min-width:0.853em;height:1.08em;",[1025,1829,1831],{"xmlns":1027,"width":1028,"height":1830,"viewBox":1548,"preserveAspectRatio":1031},"1.08em",[1033,1832],{"d":1551},[572,1834,1000],{"className":1835},[999],[572,1837,1839],{"className":1838},[908],[572,1840,1843],{"className":1841,"style":1842},[912],"height:0.2397em;",[572,1844],{},[572,1846],{"className":1847,"style":667},[666],[572,1849,1747],{"className":1850},[671],[572,1852],{"className":1853,"style":667},[666],[572,1855,1857,1860],{"className":1856},[606],[572,1858],{"className":1859,"style":681},[610],[572,1861,646],{"className":1862},[615],", ebenso ",[572,1865,1867,1894],{"className":1866},[575],[572,1868,1870],{"className":1869},[579],[581,1871,1872],{"xmlns":583},[585,1873,1874,1891],{},[588,1875,1876,1887,1889],{},[852,1877,1878,1885],{},[1242,1879,1880,1882],{},[591,1881,593],{},[591,1883,1884],{},"k",[591,1886,593],{},[640,1888,1747],{},[644,1890,646],{},[595,1892,1893],{"encoding":597},"\\sqrt[n]{n^k} \\to 1",[572,1895,1897,2020],{"className":1896,"ariaHidden":602},[601],[572,1898,1900,1904,2011,2014,2017],{"className":1899},[606],[572,1901],{"className":1902,"style":1903},[610],"height:1.04em;vertical-align:-0.0674em;",[572,1905,1907,1935],{"className":1906},[615,896],[572,1908,1910],{"className":1909},[900],[572,1911,1913],{"className":1912},[904],[572,1914,1916],{"className":1915},[908],[572,1917,1920],{"className":1918,"style":1919},[912],"height:0.7583em;",[572,1921,1923,1926],{"style":1922},"top:-3.0431em;",[572,1924],{"className":1925,"style":921},[920],[572,1927,1929],{"className":1928},[925,926,927,928],[572,1930,1932],{"className":1931},[615,928],[572,1933,593],{"className":1934},[615,616,928],[572,1936,1938,2002],{"className":1937},[904,938],[572,1939,1941,1999],{"className":1940},[908],[572,1942,1945,1986],{"className":1943,"style":1944},[912],"height:0.9726em;",[572,1946,1948,1951],{"className":1947,"style":1807},[949],[572,1949],{"className":1950,"style":1407},[920],[572,1952,1954],{"className":1953,"style":1814},[615],[572,1955,1957,1960],{"className":1956},[615],[572,1958,593],{"className":1959},[615,616],[572,1961,1963],{"className":1962},[971],[572,1964,1966],{"className":1965},[904],[572,1967,1969],{"className":1968},[908],[572,1970,1973],{"className":1971,"style":1972},[912],"height:0.7751em;",[572,1974,1976,1979],{"style":1975},"top:-2.989em;margin-right:0.05em;",[572,1977],{"className":1978,"style":988},[920],[572,1980,1982],{"className":1981},[925,926,992,928],[572,1983,1884],{"className":1984,"style":1985},[615,616,928],"margin-right:0.0315em;",[572,1987,1989,1992],{"style":1988},"top:-2.9326em;",[572,1990],{"className":1991,"style":1407},[920],[572,1993,1995],{"className":1994,"style":1827},[1022],[1025,1996,1997],{"xmlns":1027,"width":1028,"height":1830,"viewBox":1548,"preserveAspectRatio":1031},[1033,1998],{"d":1551},[572,2000,1000],{"className":2001},[999],[572,2003,2005],{"className":2004},[908],[572,2006,2009],{"className":2007,"style":2008},[912],"height:0.0674em;",[572,2010],{},[572,2012],{"className":2013,"style":667},[666],[572,2015,1747],{"className":2016},[671],[572,2018],{"className":2019,"style":667},[666],[572,2021,2023,2026],{"className":2022},[606],[572,2024],{"className":2025,"style":681},[610],[572,2027,646],{"className":2028},[615]," für festes ",[572,2031,2033,2046],{"className":2032},[575],[572,2034,2036],{"className":2035},[579],[581,2037,2038],{"xmlns":583},[585,2039,2040,2044],{},[588,2041,2042],{},[591,2043,1884],{},[595,2045,1884],{"encoding":597},[572,2047,2049],{"className":2048,"ariaHidden":602},[601],[572,2050,2052,2056],{"className":2051},[606],[572,2053],{"className":2054,"style":2055},[610],"height:0.6944em;",[572,2057,1884],{"className":2058,"style":1985},[615,616],[559,2060,2062],{"id":2061},"beispiele","Beispiele",[564,2064,2065,2251,2252,2280],{},[572,2066,2068,2108],{"className":2067},[575],[572,2069,2071],{"className":2070},[579],[581,2072,2073],{"xmlns":583},[585,2074,2075,2105],{},[588,2076,2077,2079],{},[640,2078,1620],{},[1242,2080,2081,2103],{},[588,2082,2083,2085,2101],{},[640,2084,1237],{"fence":602},[1321,2086,2087,2089],{},[591,2088,593],{},[588,2090,2091,2094,2096,2099],{},[644,2092,2093],{},"2",[591,2095,593],{},[640,2097,2098],{},"+",[644,2100,646],{},[640,2102,1246],{"fence":602},[591,2104,593],{},[595,2106,2107],{"encoding":597},"\\sum \\left(\\frac{n}{2n + 1}\\right)^n",[572,2109,2111],{"className":2110,"ariaHidden":602},[601],[572,2112,2114,2118,2121,2124],{"className":2113},[606],[572,2115],{"className":2116,"style":2117},[610],"height:1.3076em;vertical-align:-0.4033em;",[572,2119,1620],{"className":2120,"style":1651},[888,1649,1650],[572,2122],{"className":2123,"style":892},[666],[572,2125,2127,2226],{"className":2126},[1269],[572,2128,2130,2139,2220],{"className":2129},[1269],[572,2131,2135],{"className":2132,"style":2134},[1265,2133],"delimcenter","top:0em;",[572,2136,1237],{"className":2137},[2138,927],"delimsizing",[572,2140,2142,2145,2217],{"className":2141},[615],[572,2143],{"className":2144},[1265,1387],[572,2146,2148],{"className":2147},[1321],[572,2149,2151,2208],{"className":2150},[904,938],[572,2152,2154,2205],{"className":2153},[908],[572,2155,2158,2183,2191],{"className":2156,"style":2157},[912],"height:0.6954em;",[572,2159,2161,2164],{"style":2160},"top:-2.655em;",[572,2162],{"className":2163,"style":1407},[920],[572,2165,2167],{"className":2166},[925,926,992,928],[572,2168,2170,2173,2176,2180],{"className":2169},[615,928],[572,2171,2093],{"className":2172},[615,928],[572,2174,593],{"className":2175},[615,616,928],[572,2177,2098],{"className":2178},[2179,928],"mbin",[572,2181,646],{"className":2182},[615,928],[572,2184,2185,2188],{"style":1566},[572,2186],{"className":2187,"style":1407},[920],[572,2189],{"className":2190,"style":1574},[1573],[572,2192,2193,2196],{"style":1577},[572,2194],{"className":2195,"style":1407},[920],[572,2197,2199],{"className":2198},[925,926,992,928],[572,2200,2202],{"className":2201},[615,928],[572,2203,593],{"className":2204},[615,616,928],[572,2206,1000],{"className":2207},[999],[572,2209,2211],{"className":2210},[908],[572,2212,2215],{"className":2213,"style":2214},[912],"height:0.4033em;",[572,2216],{},[572,2218],{"className":2219},[1273,1387],[572,2221,2223],{"className":2222,"style":2134},[1273,2133],[572,2224,1246],{"className":2225},[2138,927],[572,2227,2229],{"className":2228},[971],[572,2230,2232],{"className":2231},[904],[572,2233,2235],{"className":2234},[908],[572,2236,2239],{"className":2237,"style":2238},[912],"height:0.9043em;",[572,2240,2242,2245],{"style":2241},"top:-3.3029em;margin-right:0.05em;",[572,2243],{"className":2244,"style":988},[920],[572,2246,2248],{"className":2247},[925,926,992,928],[572,2249,593],{"className":2250},[615,616,928],": Die ",[572,2253,2255,2268],{"className":2254},[575],[572,2256,2258],{"className":2257},[579],[581,2259,2260],{"xmlns":583},[585,2261,2262,2266],{},[588,2263,2264],{},[591,2265,593],{},[595,2267,593],{"encoding":597},[572,2269,2271],{"className":2270,"ariaHidden":602},[601],[572,2272,2274,2277],{"className":2273},[606],[572,2275],{"className":2276,"style":611},[610],[572,2278,593],{"className":2279},[615,616],"-te Wurzel hebt die Potenz auf,",[572,2282,2285],{"className":2283},[2284],"katex-display",[572,2286,2288,2357],{"className":2287},[575],[572,2289,2291],{"className":2290},[579],[581,2292,2294],{"xmlns":583,"display":2293},"block",[585,2295,2296,2354],{},[588,2297,2298,2326,2328,2342,2344,2350,2352],{},[852,2299,2300,2324],{},[1242,2301,2302,2322],{},[588,2303,2304,2306,2320],{},[640,2305,1237],{"fence":602},[1321,2307,2308,2310],{},[591,2309,593],{},[588,2311,2312,2314,2316,2318],{},[644,2313,2093],{},[591,2315,593],{},[640,2317,2098],{},[644,2319,646],{},[640,2321,1246],{"fence":602},[591,2323,593],{},[591,2325,593],{},[640,2327,792],{},[1321,2329,2330,2332],{},[591,2331,593],{},[588,2333,2334,2336,2338,2340],{},[644,2335,2093],{},[591,2337,593],{},[640,2339,2098],{},[644,2341,646],{},[640,2343,1747],{},[1321,2345,2346,2348],{},[644,2347,646],{},[644,2349,2093],{},[640,2351,642],{},[644,2353,646],{},[595,2355,2356],{"encoding":597},"\\sqrt[n]{\\left(\\frac{n}{2n + 1}\\right)^n} = \\frac{n}{2n + 1} \\to \\frac{1}{2} \u003C 1",[572,2358,2360,2582,2675,2755],{"className":2359,"ariaHidden":602},[601],[572,2361,2363,2367,2573,2576,2579],{"className":2362},[606],[572,2364],{"className":2365,"style":2366},[610],"height:3.04em;vertical-align:-1.129em;",[572,2368,2370,2398],{"className":2369},[615,896],[572,2371,2373],{"className":2372},[900],[572,2374,2376],{"className":2375},[904],[572,2377,2379],{"className":2378},[908],[572,2380,2383],{"className":2381,"style":2382},[912],"height:0.6845em;",[572,2384,2386,2389],{"style":2385},"top:-2.9692em;",[572,2387],{"className":2388,"style":921},[920],[572,2390,2392],{"className":2391},[925,926,927,928],[572,2393,2395],{"className":2394},[615,928],[572,2396,593],{"className":2397},[615,616,928],[572,2399,2401,2564],{"className":2400},[904,938],[572,2402,2404,2561],{"className":2403},[908],[572,2405,2408,2544],{"className":2406,"style":2407},[912],"height:1.911em;",[572,2409,2412,2416],{"className":2410,"style":2411},[949],"top:-5em;",[572,2413],{"className":2414,"style":2415},[920],"height:5em;",[572,2417,2419],{"className":2418,"style":958},[615],[572,2420,2422,2519],{"className":2421},[1269],[572,2423,2425,2431,2513],{"className":2424},[1269],[572,2426,2428],{"className":2427,"style":2134},[1265,2133],[572,2429,1237],{"className":2430},[2138,992],[572,2432,2434,2437,2510],{"className":2433},[615],[572,2435],{"className":2436},[1265,1387],[572,2438,2440],{"className":2439},[1321],[572,2441,2443,2501],{"className":2442},[904,938],[572,2444,2446,2498],{"className":2445},[908],[572,2447,2450,2478,2486],{"className":2448,"style":2449},[912],"height:1.1076em;",[572,2451,2453,2456],{"style":2452},"top:-2.314em;",[572,2454],{"className":2455,"style":1407},[920],[572,2457,2459,2462,2465,2469,2472,2475],{"className":2458},[615],[572,2460,2093],{"className":2461},[615],[572,2463,593],{"className":2464},[615,616],[572,2466],{"className":2467,"style":2468},[666],"margin-right:0.2222em;",[572,2470,2098],{"className":2471},[2179],[572,2473],{"className":2474,"style":2468},[666],[572,2476,646],{"className":2477},[615],[572,2479,2480,2483],{"style":1566},[572,2481],{"className":2482,"style":1407},[920],[572,2484],{"className":2485,"style":1574},[1573],[572,2487,2489,2492],{"style":2488},"top:-3.677em;",[572,2490],{"className":2491,"style":1407},[920],[572,2493,2495],{"className":2494},[615],[572,2496,593],{"className":2497},[615,616],[572,2499,1000],{"className":2500},[999],[572,2502,2504],{"className":2503},[908],[572,2505,2508],{"className":2506,"style":2507},[912],"height:0.7693em;",[572,2509],{},[572,2511],{"className":2512},[1273,1387],[572,2514,2516],{"className":2515,"style":2134},[1273,2133],[572,2517,1246],{"className":2518},[2138,992],[572,2520,2522],{"className":2521},[971],[572,2523,2525],{"className":2524},[904],[572,2526,2528],{"className":2527},[908],[572,2529,2532],{"className":2530,"style":2531},[912],"height:1.5043em;",[572,2533,2535,2538],{"style":2534},"top:-3.9029em;margin-right:0.05em;",[572,2536],{"className":2537,"style":988},[920],[572,2539,2541],{"className":2540},[925,926,992,928],[572,2542,593],{"className":2543},[615,616,928],[572,2545,2547,2550],{"style":2546},"top:-3.871em;",[572,2548],{"className":2549,"style":2415},[920],[572,2551,2554],{"className":2552,"style":2553},[1022],"min-width:1.02em;height:3.08em;",[1025,2555,2558],{"xmlns":1027,"width":1028,"height":2556,"viewBox":2557,"preserveAspectRatio":1031},"3.08em","0 0 400000 3240",[1033,2559],{"d":2560},"M473,2793\nc339.3,-1799.3,509.3,-2700,510,-2702 l0 -0\nc3.3,-7.3,9.3,-11,18,-11 H400000v40H1017.7\ns-90.5,478,-276.2,1466c-185.7,988,-279.5,1483,-281.5,1485c-2,6,-10,9,-24,9\nc-8,0,-12,-0.7,-12,-2c0,-1.3,-5.3,-32,-16,-92c-50.7,-293.3,-119.7,-693.3,-207,-1200\nc0,-1.3,-5.3,8.7,-16,30c-10.7,21.3,-21.3,42.7,-32,64s-16,33,-16,33s-26,-26,-26,-26\ns76,-153,76,-153s77,-151,77,-151c0.7,0.7,35.7,202,105,604c67.3,400.7,102,602.7,104,\n606zM1001 80h400000v40H1017.7z",[572,2562,1000],{"className":2563},[999],[572,2565,2567],{"className":2566},[908],[572,2568,2571],{"className":2569,"style":2570},[912],"height:1.129em;",[572,2572],{},[572,2574],{"className":2575,"style":667},[666],[572,2577,792],{"className":2578},[671],[572,2580],{"className":2581,"style":667},[666],[572,2583,2585,2589,2666,2669,2672],{"className":2584},[606],[572,2586],{"className":2587,"style":2588},[610],"height:1.8769em;vertical-align:-0.7693em;",[572,2590,2592,2595,2663],{"className":2591},[615],[572,2593],{"className":2594},[1265,1387],[572,2596,2598],{"className":2597},[1321],[572,2599,2601,2655],{"className":2600},[904,938],[572,2602,2604,2652],{"className":2603},[908],[572,2605,2607,2633,2641],{"className":2606,"style":2449},[912],[572,2608,2609,2612],{"style":2452},[572,2610],{"className":2611,"style":1407},[920],[572,2613,2615,2618,2621,2624,2627,2630],{"className":2614},[615],[572,2616,2093],{"className":2617},[615],[572,2619,593],{"className":2620},[615,616],[572,2622],{"className":2623,"style":2468},[666],[572,2625,2098],{"className":2626},[2179],[572,2628],{"className":2629,"style":2468},[666],[572,2631,646],{"className":2632},[615],[572,2634,2635,2638],{"style":1566},[572,2636],{"className":2637,"style":1407},[920],[572,2639],{"className":2640,"style":1574},[1573],[572,2642,2643,2646],{"style":2488},[572,2644],{"className":2645,"style":1407},[920],[572,2647,2649],{"className":2648},[615],[572,2650,593],{"className":2651},[615,616],[572,2653,1000],{"className":2654},[999],[572,2656,2658],{"className":2657},[908],[572,2659,2661],{"className":2660,"style":2507},[912],[572,2662],{},[572,2664],{"className":2665},[1273,1387],[572,2667],{"className":2668,"style":667},[666],[572,2670,1747],{"className":2671},[671],[572,2673],{"className":2674,"style":667},[666],[572,2676,2678,2682,2746,2749,2752],{"className":2677},[606],[572,2679],{"className":2680,"style":2681},[610],"height:2.0074em;vertical-align:-0.686em;",[572,2683,2685,2688,2743],{"className":2684},[615],[572,2686],{"className":2687},[1265,1387],[572,2689,2691],{"className":2690},[1321],[572,2692,2694,2734],{"className":2693},[904,938],[572,2695,2697,2731],{"className":2696},[908],[572,2698,2701,2712,2720],{"className":2699,"style":2700},[912],"height:1.3214em;",[572,2702,2703,2706],{"style":2452},[572,2704],{"className":2705,"style":1407},[920],[572,2707,2709],{"className":2708},[615],[572,2710,2093],{"className":2711},[615],[572,2713,2714,2717],{"style":1566},[572,2715],{"className":2716,"style":1407},[920],[572,2718],{"className":2719,"style":1574},[1573],[572,2721,2722,2725],{"style":2488},[572,2723],{"className":2724,"style":1407},[920],[572,2726,2728],{"className":2727},[615],[572,2729,646],{"className":2730},[615],[572,2732,1000],{"className":2733},[999],[572,2735,2737],{"className":2736},[908],[572,2738,2741],{"className":2739,"style":2740},[912],"height:0.686em;",[572,2742],{},[572,2744],{"className":2745},[1273,1387],[572,2747],{"className":2748,"style":667},[666],[572,2750,642],{"className":2751},[671],[572,2753],{"className":2754,"style":667},[666],[572,2756,2758,2761],{"className":2757},[606],[572,2759],{"className":2760,"style":681},[610],[572,2762,646],{"className":2763},[615],[564,2765,2766],{},"Die Reihe konvergiert absolut.",[564,2768,2769,2943,2944,3106],{},[572,2770,2772,2801],{"className":2771},[575],[572,2773,2775],{"className":2774},[579],[581,2776,2777],{"xmlns":583},[585,2778,2779,2798],{},[588,2780,2781,2783],{},[640,2782,1620],{},[1321,2784,2785,2791],{},[1242,2786,2787,2789],{},[591,2788,593],{},[644,2790,2093],{},[1242,2792,2793,2796],{},[644,2794,2795],{},"3",[591,2797,593],{},[595,2799,2800],{"encoding":597},"\\sum \\frac{n^2}{3^n}",[572,2802,2804],{"className":2803,"ariaHidden":602},[601],[572,2805,2807,2811,2814,2817],{"className":2806},[606],[572,2808],{"className":2809,"style":2810},[610],"height:1.3629em;vertical-align:-0.345em;",[572,2812,1620],{"className":2813,"style":1651},[888,1649,1650],[572,2815],{"className":2816,"style":892},[666],[572,2818,2820,2823,2940],{"className":2819},[615],[572,2821],{"className":2822},[1265,1387],[572,2824,2826],{"className":2825},[1321],[572,2827,2829,2931],{"className":2828},[904,938],[572,2830,2832,2928],{"className":2831},[908],[572,2833,2836,2878,2886],{"className":2834,"style":2835},[912],"height:1.0179em;",[572,2837,2838,2841],{"style":2160},[572,2839],{"className":2840,"style":1407},[920],[572,2842,2844],{"className":2843},[925,926,992,928],[572,2845,2847],{"className":2846},[615,928],[572,2848,2850,2853],{"className":2849},[615,928],[572,2851,2795],{"className":2852},[615,928],[572,2854,2856],{"className":2855},[971],[572,2857,2859],{"className":2858},[904],[572,2860,2862],{"className":2861},[908],[572,2863,2866],{"className":2864,"style":2865},[912],"height:0.5935em;",[572,2867,2869,2872],{"style":2868},"top:-2.786em;margin-right:0.0714em;",[572,2870],{"className":2871,"style":921},[920],[572,2873,2875],{"className":2874},[925,1457,927,928],[572,2876,593],{"className":2877},[615,616,928],[572,2879,2880,2883],{"style":1566},[572,2881],{"className":2882,"style":1407},[920],[572,2884],{"className":2885,"style":1574},[1573],[572,2887,2888,2891],{"style":1577},[572,2889],{"className":2890,"style":1407},[920],[572,2892,2894],{"className":2893},[925,926,992,928],[572,2895,2897],{"className":2896},[615,928],[572,2898,2900,2903],{"className":2899},[615,928],[572,2901,593],{"className":2902},[615,616,928],[572,2904,2906],{"className":2905},[971],[572,2907,2909],{"className":2908},[904],[572,2910,2912],{"className":2911},[908],[572,2913,2916],{"className":2914,"style":2915},[912],"height:0.8913em;",[572,2917,2919,2922],{"style":2918},"top:-2.931em;margin-right:0.0714em;",[572,2920],{"className":2921,"style":921},[920],[572,2923,2925],{"className":2924},[925,1457,927,928],[572,2926,2093],{"className":2927},[615,928],[572,2929,1000],{"className":2930},[999],[572,2932,2934],{"className":2933},[908],[572,2935,2938],{"className":2936,"style":2937},[912],"height:0.345em;",[572,2939],{},[572,2941],{"className":2942},[1273,1387],": Wegen ",[572,2945,2947,2973],{"className":2946},[575],[572,2948,2950],{"className":2949},[579],[581,2951,2952],{"xmlns":583},[585,2953,2954,2970],{},[588,2955,2956,2966,2968],{},[852,2957,2958,2964],{},[1242,2959,2960,2962],{},[591,2961,593],{},[644,2963,2093],{},[591,2965,593],{},[640,2967,1747],{},[644,2969,646],{},[595,2971,2972],{"encoding":597},"\\sqrt[n]{n^2} \\to 1",[572,2974,2976,3097],{"className":2975,"ariaHidden":602},[601],[572,2977,2979,2983,3088,3091,3094],{"className":2978},[606],[572,2980],{"className":2981,"style":2982},[610],"height:1.04em;vertical-align:-0.0849em;",[572,2984,2986,3014],{"className":2985},[615,896],[572,2987,2989],{"className":2988},[900],[572,2990,2992],{"className":2991},[904],[572,2993,2995],{"className":2994},[908],[572,2996,2999],{"className":2997,"style":2998},[912],"height:0.7373em;",[572,3000,3002,3005],{"style":3001},"top:-3.0221em;",[572,3003],{"className":3004,"style":921},[920],[572,3006,3008],{"className":3007},[925,926,927,928],[572,3009,3011],{"className":3010},[615,928],[572,3012,593],{"className":3013},[615,616,928],[572,3015,3017,3079],{"className":3016},[904,938],[572,3018,3020,3076],{"className":3019},[908],[572,3021,3024,3063],{"className":3022,"style":3023},[912],"height:0.9551em;",[572,3025,3027,3030],{"className":3026,"style":1807},[949],[572,3028],{"className":3029,"style":1407},[920],[572,3031,3033],{"className":3032,"style":1814},[615],[572,3034,3036,3039],{"className":3035},[615],[572,3037,593],{"className":3038},[615,616],[572,3040,3042],{"className":3041},[971],[572,3043,3045],{"className":3044},[904],[572,3046,3048],{"className":3047},[908],[572,3049,3052],{"className":3050,"style":3051},[912],"height:0.7401em;",[572,3053,3054,3057],{"style":1975},[572,3055],{"className":3056,"style":988},[920],[572,3058,3060],{"className":3059},[925,926,992,928],[572,3061,2093],{"className":3062},[615,928],[572,3064,3066,3069],{"style":3065},"top:-2.9151em;",[572,3067],{"className":3068,"style":1407},[920],[572,3070,3072],{"className":3071,"style":1827},[1022],[1025,3073,3074],{"xmlns":1027,"width":1028,"height":1830,"viewBox":1548,"preserveAspectRatio":1031},[1033,3075],{"d":1551},[572,3077,1000],{"className":3078},[999],[572,3080,3082],{"className":3081},[908],[572,3083,3086],{"className":3084,"style":3085},[912],"height:0.0849em;",[572,3087],{},[572,3089],{"className":3090,"style":667},[666],[572,3092,1747],{"className":3093},[671],[572,3095],{"className":3096,"style":667},[666],[572,3098,3100,3103],{"className":3099},[606],[572,3101],{"className":3102,"style":681},[610],[572,3104,646],{"className":3105},[615]," gilt",[572,3108,3110],{"className":3109},[2284],[572,3111,3113,3171],{"className":3112},[575],[572,3114,3116],{"className":3115},[579],[581,3117,3118],{"xmlns":583,"display":2293},[585,3119,3120,3168],{},[588,3121,3122,3140,3142,3156,3158,3164,3166],{},[852,3123,3124,3138],{},[1321,3125,3126,3132],{},[1242,3127,3128,3130],{},[591,3129,593],{},[644,3131,2093],{},[1242,3133,3134,3136],{},[644,3135,2795],{},[591,3137,593],{},[591,3139,593],{},[640,3141,792],{},[1321,3143,3144,3154],{},[852,3145,3146,3152],{},[1242,3147,3148,3150],{},[591,3149,593],{},[644,3151,2093],{},[591,3153,593],{},[644,3155,2795],{},[640,3157,1747],{},[1321,3159,3160,3162],{},[644,3161,646],{},[644,3163,2795],{},[640,3165,642],{},[644,3167,646],{},[595,3169,3170],{"encoding":597},"\\sqrt[n]{\\frac{n^2}{3^n}} = \\frac{\\sqrt[n]{n^2}}{3} \\to \\frac{1}{3} \u003C 1",[572,3172,3174,3387,3562,3639],{"className":3173,"ariaHidden":602},[601],[572,3175,3177,3181,3378,3381,3384],{"className":3176},[606],[572,3178],{"className":3179,"style":3180},[610],"height:2.44em;vertical-align:-0.7406em;",[572,3182,3184,3212],{"className":3183},[615,896],[572,3185,3187],{"className":3186},[900],[572,3188,3190],{"className":3189},[904],[572,3191,3193],{"className":3192},[908],[572,3194,3197],{"className":3195,"style":3196},[912],"height:0.7906em;",[572,3198,3200,3203],{"style":3199},"top:-3.0753em;",[572,3201],{"className":3202,"style":921},[920],[572,3204,3206],{"className":3205},[925,926,927,928],[572,3207,3209],{"className":3208},[615,928],[572,3210,593],{"className":3211},[615,616,928],[572,3213,3215,3369],{"className":3214},[904,938],[572,3216,3218,3366],{"className":3217},[908],[572,3219,3222,3349],{"className":3220,"style":3221},[912],"height:1.6994em;",[572,3223,3226,3230],{"className":3224,"style":3225},[949],"top:-4.4em;",[572,3227],{"className":3228,"style":3229},[920],"height:4.4em;",[572,3231,3233],{"className":3232,"style":958},[615],[572,3234,3236,3239,3346],{"className":3235},[615],[572,3237],{"className":3238},[1265,1387],[572,3240,3242],{"className":3241},[1321],[572,3243,3245,3338],{"className":3244},[904,938],[572,3246,3248,3335],{"className":3247},[908],[572,3249,3252,3290,3298],{"className":3250,"style":3251},[912],"height:1.4171em;",[572,3253,3254,3257],{"style":2452},[572,3255],{"className":3256,"style":1407},[920],[572,3258,3260],{"className":3259},[615],[572,3261,3263,3266],{"className":3262},[615],[572,3264,2795],{"className":3265},[615],[572,3267,3269],{"className":3268},[971],[572,3270,3272],{"className":3271},[904],[572,3273,3275],{"className":3274},[908],[572,3276,3279],{"className":3277,"style":3278},[912],"height:0.5904em;",[572,3280,3281,3284],{"style":1975},[572,3282],{"className":3283,"style":988},[920],[572,3285,3287],{"className":3286},[925,926,992,928],[572,3288,593],{"className":3289},[615,616,928],[572,3291,3292,3295],{"style":1566},[572,3293],{"className":3294,"style":1407},[920],[572,3296],{"className":3297,"style":1574},[1573],[572,3299,3300,3303],{"style":2488},[572,3301],{"className":3302,"style":1407},[920],[572,3304,3306],{"className":3305},[615],[572,3307,3309,3312],{"className":3308},[615],[572,3310,593],{"className":3311},[615,616],[572,3313,3315],{"className":3314},[971],[572,3316,3318],{"className":3317},[904],[572,3319,3321],{"className":3320},[908],[572,3322,3324],{"className":3323,"style":3051},[912],[572,3325,3326,3329],{"style":1975},[572,3327],{"className":3328,"style":988},[920],[572,3330,3332],{"className":3331},[925,926,992,928],[572,3333,2093],{"className":3334},[615,928],[572,3336,1000],{"className":3337},[999],[572,3339,3341],{"className":3340},[908],[572,3342,3344],{"className":3343,"style":2740},[912],[572,3345],{},[572,3347],{"className":3348},[1273,1387],[572,3350,3352,3355],{"style":3351},"top:-3.6594em;",[572,3353],{"className":3354,"style":3229},[920],[572,3356,3359],{"className":3357,"style":3358},[1022],"min-width:1.02em;height:2.48em;",[1025,3360,3363],{"xmlns":1027,"width":1028,"height":3361,"viewBox":3362,"preserveAspectRatio":1031},"2.48em","0 0 400000 2592",[1033,3364],{"d":3365},"M424,2478\nc-1.3,-0.7,-38.5,-172,-111.5,-514c-73,-342,-109.8,-513.3,-110.5,-514\nc0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5,25c-5.7,9.3,-9.8,16,-12.5,20\ns-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13,-13s76,-122,76,-122s77,-121,77,-121\ns209,968,209,968c0,-2,84.7,-361.7,254,-1079c169.3,-717.3,254.7,-1077.7,256,-1081\nl0 -0c4,-6.7,10,-10,18,-10 H400000\nv40H1014.6\ns-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185\nc-2,6,-10,9,-24,9\nc-8,0,-12,-0.7,-12,-2z M1001 80\nh400000v40h-400000z",[572,3367,1000],{"className":3368},[999],[572,3370,3372],{"className":3371},[908],[572,3373,3376],{"className":3374,"style":3375},[912],"height:0.7406em;",[572,3377],{},[572,3379],{"className":3380,"style":667},[666],[572,3382,792],{"className":3383},[671],[572,3385],{"className":3386,"style":667},[666],[572,3388,3390,3394,3553,3556,3559],{"className":3389},[606],[572,3391],{"className":3392,"style":3393},[610],"height:2.3181em;vertical-align:-0.686em;",[572,3395,3397,3400,3550],{"className":3396},[615],[572,3398],{"className":3399},[1265,1387],[572,3401,3403],{"className":3402},[1321],[572,3404,3406,3542],{"className":3405},[904,938],[572,3407,3409,3539],{"className":3408},[908],[572,3410,3413,3424,3432],{"className":3411,"style":3412},[912],"height:1.6321em;",[572,3414,3415,3418],{"style":2452},[572,3416],{"className":3417,"style":1407},[920],[572,3419,3421],{"className":3420},[615],[572,3422,2795],{"className":3423},[615],[572,3425,3426,3429],{"style":1566},[572,3427],{"className":3428,"style":1407},[920],[572,3430],{"className":3431,"style":1574},[1573],[572,3433,3434,3437],{"style":2488},[572,3435],{"className":3436,"style":1407},[920],[572,3438,3440],{"className":3439},[615],[572,3441,3443,3469],{"className":3442},[615,896],[572,3444,3446],{"className":3445},[900],[572,3447,3449],{"className":3448},[904],[572,3450,3452],{"className":3451},[908],[572,3453,3455],{"className":3454,"style":2998},[912],[572,3456,3457,3460],{"style":3001},[572,3458],{"className":3459,"style":921},[920],[572,3461,3463],{"className":3462},[925,926,927,928],[572,3464,3466],{"className":3465},[615,928],[572,3467,593],{"className":3468},[615,616,928],[572,3470,3472,3531],{"className":3471},[904,938],[572,3473,3475,3528],{"className":3474},[908],[572,3476,3478,3516],{"className":3477,"style":3023},[912],[572,3479,3481,3484],{"className":3480,"style":1807},[949],[572,3482],{"className":3483,"style":1407},[920],[572,3485,3487],{"className":3486,"style":1814},[615],[572,3488,3490,3493],{"className":3489},[615],[572,3491,593],{"className":3492},[615,616],[572,3494,3496],{"className":3495},[971],[572,3497,3499],{"className":3498},[904],[572,3500,3502],{"className":3501},[908],[572,3503,3505],{"className":3504,"style":3051},[912],[572,3506,3507,3510],{"style":1975},[572,3508],{"className":3509,"style":988},[920],[572,3511,3513],{"className":3512},[925,926,992,928],[572,3514,2093],{"className":3515},[615,928],[572,3517,3518,3521],{"style":3065},[572,3519],{"className":3520,"style":1407},[920],[572,3522,3524],{"className":3523,"style":1827},[1022],[1025,3525,3526],{"xmlns":1027,"width":1028,"height":1830,"viewBox":1548,"preserveAspectRatio":1031},[1033,3527],{"d":1551},[572,3529,1000],{"className":3530},[999],[572,3532,3534],{"className":3533},[908],[572,3535,3537],{"className":3536,"style":3085},[912],[572,3538],{},[572,3540,1000],{"className":3541},[999],[572,3543,3545],{"className":3544},[908],[572,3546,3548],{"className":3547,"style":2740},[912],[572,3549],{},[572,3551],{"className":3552},[1273,1387],[572,3554],{"className":3555,"style":667},[666],[572,3557,1747],{"className":3558},[671],[572,3560],{"className":3561,"style":667},[666],[572,3563,3565,3568,3630,3633,3636],{"className":3564},[606],[572,3566],{"className":3567,"style":2681},[610],[572,3569,3571,3574,3627],{"className":3570},[615],[572,3572],{"className":3573},[1265,1387],[572,3575,3577],{"className":3576},[1321],[572,3578,3580,3619],{"className":3579},[904,938],[572,3581,3583,3616],{"className":3582},[908],[572,3584,3586,3597,3605],{"className":3585,"style":2700},[912],[572,3587,3588,3591],{"style":2452},[572,3589],{"className":3590,"style":1407},[920],[572,3592,3594],{"className":3593},[615],[572,3595,2795],{"className":3596},[615],[572,3598,3599,3602],{"style":1566},[572,3600],{"className":3601,"style":1407},[920],[572,3603],{"className":3604,"style":1574},[1573],[572,3606,3607,3610],{"style":2488},[572,3608],{"className":3609,"style":1407},[920],[572,3611,3613],{"className":3612},[615],[572,3614,646],{"className":3615},[615],[572,3617,1000],{"className":3618},[999],[572,3620,3622],{"className":3621},[908],[572,3623,3625],{"className":3624,"style":2740},[912],[572,3626],{},[572,3628],{"className":3629},[1273,1387],[572,3631],{"className":3632,"style":667},[666],[572,3634,642],{"className":3635},[671],[572,3637],{"className":3638,"style":667},[666],[572,3640,3642,3645],{"className":3641},[606],[572,3643],{"className":3644,"style":681},[610],[572,3646,646],{"className":3647},[615],[564,3649,3650,3651,3694,3695,3747,3748,3789],{},"Die Reihe konvergiert, ihr Wert ist ",[572,3652,3654,3669],{"className":3653},[575],[572,3655,3657],{"className":3656},[579],[581,3658,3659],{"xmlns":583},[585,3660,3661,3666],{},[588,3662,3663],{},[644,3664,3665],{},"1,5",[595,3667,3668],{"encoding":597},"1{,}5",[572,3670,3672],{"className":3671,"ariaHidden":602},[601],[572,3673,3675,3679,3682,3690],{"className":3674},[606],[572,3676],{"className":3677,"style":3678},[610],"height:0.8389em;vertical-align:-0.1944em;",[572,3680,646],{"className":3681},[615],[572,3683,3685],{"className":3684},[615],[572,3686,3689],{"className":3687},[3688],"mpunct",",",[572,3691,3693],{"className":3692},[615],"5",". Bei ",[572,3696,3698,3717],{"className":3697},[575],[572,3699,3701],{"className":3700},[579],[581,3702,3703],{"xmlns":583},[585,3704,3705,3714],{},[588,3706,3707,3709,3711],{},[591,3708,593],{},[640,3710,792],{},[644,3712,3713],{},"1000",[595,3715,3716],{"encoding":597},"n = 1000",[572,3718,3720,3738],{"className":3719,"ariaHidden":602},[601],[572,3721,3723,3726,3729,3732,3735],{"className":3722},[606],[572,3724],{"className":3725,"style":611},[610],[572,3727,593],{"className":3728},[615,616],[572,3730],{"className":3731,"style":667},[666],[572,3733,792],{"className":3734},[671],[572,3736],{"className":3737,"style":667},[666],[572,3739,3741,3744],{"className":3740},[606],[572,3742],{"className":3743,"style":681},[610],[572,3745,3713],{"className":3746},[615]," ist die Wurzel erst bei etwa ",[572,3749,3751,3766],{"className":3750},[575],[572,3752,3754],{"className":3753},[579],[581,3755,3756],{"xmlns":583},[585,3757,3758,3763],{},[588,3759,3760],{},[644,3761,3762],{},"0,3380",[595,3764,3765],{"encoding":597},"0{,}3380",[572,3767,3769],{"className":3768,"ariaHidden":602},[601],[572,3770,3772,3775,3779,3785],{"className":3771},[606],[572,3773],{"className":3774,"style":3678},[610],[572,3776,3778],{"className":3777},[615],"0",[572,3780,3782],{"className":3781},[615],[572,3783,3689],{"className":3784},[3688],[572,3786,3788],{"className":3787},[615],"3380",", der Grenzwert wird langsam erreicht.",[564,3791,3792,3928,3929,3957,3958,4058,4059,4285],{},[572,3793,3795,3834],{"className":3794},[575],[572,3796,3798],{"className":3797},[579],[581,3799,3800],{"xmlns":583},[585,3801,3802,3831],{},[588,3803,3804,3806],{},[640,3805,1620],{},[1242,3807,3808,3810],{},[644,3809,2093],{},[588,3811,3812,3815,3817,3819,3821,3823,3825],{},[640,3813,3814],{},"−",[591,3816,593],{},[640,3818,2098],{},[640,3820,1237],{"stretchy":1236},[640,3822,3814],{},[644,3824,646],{},[1242,3826,3827,3829],{},[640,3828,1246],{"stretchy":1236},[591,3830,593],{},[595,3832,3833],{"encoding":597},"\\sum 2^{-n + (-1)^n}",[572,3835,3837],{"className":3836,"ariaHidden":602},[601],[572,3838,3840,3844,3847,3850],{"className":3839},[606],[572,3841],{"className":3842,"style":3843},[610],"height:1.138em;vertical-align:-0.25em;",[572,3845,1620],{"className":3846,"style":1651},[888,1649,1650],[572,3848],{"className":3849,"style":892},[666],[572,3851,3853,3856],{"className":3852},[615],[572,3854,2093],{"className":3855},[615],[572,3857,3859],{"className":3858},[971],[572,3860,3862],{"className":3861},[904],[572,3863,3865],{"className":3864},[908],[572,3866,3869],{"className":3867,"style":3868},[912],"height:0.888em;",[572,3870,3871,3874],{"style":1292},[572,3872],{"className":3873,"style":988},[920],[572,3875,3877],{"className":3876},[925,926,992,928],[572,3878,3880,3883,3886,3889,3892,3895,3898],{"className":3879},[615,928],[572,3881,3814],{"className":3882},[615,928],[572,3884,593],{"className":3885},[615,616,928],[572,3887,2098],{"className":3888},[2179,928],[572,3890,1237],{"className":3891},[1265,928],[572,3893,3814],{"className":3894},[615,928],[572,3896,646],{"className":3897},[615,928],[572,3899,3901,3904],{"className":3900},[1273,928],[572,3902,1246],{"className":3903},[1273,928],[572,3905,3907],{"className":3906},[971],[572,3908,3910],{"className":3909},[904],[572,3911,3913],{"className":3912},[908],[572,3914,3917],{"className":3915,"style":3916},[912],"height:0.7385em;",[572,3918,3919,3922],{"style":2918},[572,3920],{"className":3921,"style":921},[920],[572,3923,3925],{"className":3924},[925,1457,927,928],[572,3926,593],{"className":3927},[615,616,928],": Der Quotient aufeinanderfolgender Glieder springt zwischen ",[572,3930,3932,3945],{"className":3931},[575],[572,3933,3935],{"className":3934},[579],[581,3936,3937],{"xmlns":583},[585,3938,3939,3943],{},[588,3940,3941],{},[644,3942,2093],{},[595,3944,2093],{"encoding":597},[572,3946,3948],{"className":3947,"ariaHidden":602},[601],[572,3949,3951,3954],{"className":3950},[606],[572,3952],{"className":3953,"style":681},[610],[572,3955,2093],{"className":3956},[615]," und ",[572,3959,3961,3980],{"className":3960},[575],[572,3962,3964],{"className":3963},[579],[581,3965,3966],{"xmlns":583},[585,3967,3968,3977],{},[588,3969,3970],{},[1321,3971,3972,3974],{},[644,3973,646],{},[644,3975,3976],{},"8",[595,3978,3979],{"encoding":597},"\\frac{1}{8}",[572,3981,3983],{"className":3982,"ariaHidden":602},[601],[572,3984,3986,3990],{"className":3985},[606],[572,3987],{"className":3988,"style":3989},[610],"height:1.1901em;vertical-align:-0.345em;",[572,3991,3993,3996,4055],{"className":3992},[615],[572,3994],{"className":3995},[1265,1387],[572,3997,3999],{"className":3998},[1321],[572,4000,4002,4047],{"className":4001},[904,938],[572,4003,4005,4044],{"className":4004},[908],[572,4006,4008,4022,4030],{"className":4007,"style":1400},[912],[572,4009,4010,4013],{"style":2160},[572,4011],{"className":4012,"style":1407},[920],[572,4014,4016],{"className":4015},[925,926,992,928],[572,4017,4019],{"className":4018},[615,928],[572,4020,3976],{"className":4021},[615,928],[572,4023,4024,4027],{"style":1566},[572,4025],{"className":4026,"style":1407},[920],[572,4028],{"className":4029,"style":1574},[1573],[572,4031,4032,4035],{"style":1577},[572,4033],{"className":4034,"style":1407},[920],[572,4036,4038],{"className":4037},[925,926,992,928],[572,4039,4041],{"className":4040},[615,928],[572,4042,646],{"className":4043},[615,928],[572,4045,1000],{"className":4046},[999],[572,4048,4050],{"className":4049},[908],[572,4051,4053],{"className":4052,"style":2937},[912],[572,4054],{},[572,4056],{"className":4057},[1273,1387]," hin und her, das Quotientenkriterium entscheidet nicht. Die Wurzel ist ",[572,4060,4062,4111],{"className":4061},[575],[572,4063,4065],{"className":4064},[579],[581,4066,4067],{"xmlns":583},[585,4068,4069,4108],{},[588,4070,4071,4100,4102],{},[1242,4072,4073,4075],{},[644,4074,2093],{},[588,4076,4077,4079,4081,4083,4085,4087,4089,4095,4098],{},[640,4078,3814],{},[644,4080,646],{},[640,4082,2098],{},[640,4084,1237],{"stretchy":1236},[640,4086,3814],{},[644,4088,646],{},[1242,4090,4091,4093],{},[640,4092,1246],{"stretchy":1236},[591,4094,593],{},[591,4096,4097],{"mathvariant":858},"\u002F",[591,4099,593],{},[640,4101,1747],{},[1321,4103,4104,4106],{},[644,4105,646],{},[644,4107,2093],{},[595,4109,4110],{"encoding":597},"2^{-1 + (-1)^n \u002F n} \\to \\frac{1}{2}",[572,4112,4114,4211],{"className":4113,"ariaHidden":602},[601],[572,4115,4117,4120,4202,4205,4208],{"className":4116},[606],[572,4118],{"className":4119,"style":3868},[610],[572,4121,4123,4126],{"className":4122},[615],[572,4124,2093],{"className":4125},[615],[572,4127,4129],{"className":4128},[971],[572,4130,4132],{"className":4131},[904],[572,4133,4135],{"className":4134},[908],[572,4136,4138],{"className":4137,"style":3868},[912],[572,4139,4140,4143],{"style":1292},[572,4141],{"className":4142,"style":988},[920],[572,4144,4146],{"className":4145},[925,926,992,928],[572,4147,4149,4152,4155,4158,4161,4164,4167,4196,4199],{"className":4148},[615,928],[572,4150,3814],{"className":4151},[615,928],[572,4153,646],{"className":4154},[615,928],[572,4156,2098],{"className":4157},[2179,928],[572,4159,1237],{"className":4160},[1265,928],[572,4162,3814],{"className":4163},[615,928],[572,4165,646],{"className":4166},[615,928],[572,4168,4170,4173],{"className":4169},[1273,928],[572,4171,1246],{"className":4172},[1273,928],[572,4174,4176],{"className":4175},[971],[572,4177,4179],{"className":4178},[904],[572,4180,4182],{"className":4181},[908],[572,4183,4185],{"className":4184,"style":3916},[912],[572,4186,4187,4190],{"style":2918},[572,4188],{"className":4189,"style":921},[920],[572,4191,4193],{"className":4192},[925,1457,927,928],[572,4194,593],{"className":4195},[615,616,928],[572,4197,4097],{"className":4198},[615,928],[572,4200,593],{"className":4201},[615,616,928],[572,4203],{"className":4204,"style":667},[666],[572,4206,1747],{"className":4207},[671],[572,4209],{"className":4210,"style":667},[666],[572,4212,4214,4217],{"className":4213},[606],[572,4215],{"className":4216,"style":3989},[610],[572,4218,4220,4223,4282],{"className":4219},[615],[572,4221],{"className":4222},[1265,1387],[572,4224,4226],{"className":4225},[1321],[572,4227,4229,4274],{"className":4228},[904,938],[572,4230,4232,4271],{"className":4231},[908],[572,4233,4235,4249,4257],{"className":4234,"style":1400},[912],[572,4236,4237,4240],{"style":2160},[572,4238],{"className":4239,"style":1407},[920],[572,4241,4243],{"className":4242},[925,926,992,928],[572,4244,4246],{"className":4245},[615,928],[572,4247,2093],{"className":4248},[615,928],[572,4250,4251,4254],{"style":1566},[572,4252],{"className":4253,"style":1407},[920],[572,4255],{"className":4256,"style":1574},[1573],[572,4258,4259,4262],{"style":1577},[572,4260],{"className":4261,"style":1407},[920],[572,4263,4265],{"className":4264},[925,926,992,928],[572,4266,4268],{"className":4267},[615,928],[572,4269,646],{"className":4270},[615,928],[572,4272,1000],{"className":4273},[999],[572,4275,4277],{"className":4276},[908],[572,4278,4280],{"className":4279,"style":2937},[912],[572,4281],{},[572,4283],{"className":4284},[1273,1387],", also konvergiert die Reihe.",[559,4287,4289],{"id":4288},"typische-fehler","Typische Fehler",[619,4291,4292,4641,4765,5017],{},[622,4293,4294,4295,4345,4346,3957,4452,4589,4590,4640],{},"Aus ",[572,4296,4298,4315],{"className":4297},[575],[572,4299,4301],{"className":4300},[579],[581,4302,4303],{"xmlns":583},[585,4304,4305,4313],{},[588,4306,4307,4309,4311],{},[591,4308,638],{},[640,4310,792],{},[644,4312,646],{},[595,4314,797],{"encoding":597},[572,4316,4318,4336],{"className":4317,"ariaHidden":602},[601],[572,4319,4321,4324,4327,4330,4333],{"className":4320},[606],[572,4322],{"className":4323,"style":807},[610],[572,4325,638],{"className":4326},[615,616],[572,4328],{"className":4329,"style":667},[666],[572,4331,792],{"className":4332},[671],[572,4334],{"className":4335,"style":667},[666],[572,4337,4339,4342],{"className":4338},[606],[572,4340],{"className":4341,"style":681},[610],[572,4343,646],{"className":4344},[615]," eine Aussage ableiten. Für ",[572,4347,4349,4369],{"className":4348},[575],[572,4350,4352],{"className":4351},[579],[581,4353,4354],{"xmlns":583},[585,4355,4356,4366],{},[588,4357,4358,4360],{},[640,4359,1620],{},[1321,4361,4362,4364],{},[644,4363,646],{},[591,4365,593],{},[595,4367,4368],{"encoding":597},"\\sum \\frac{1}{n}",[572,4370,4372],{"className":4371,"ariaHidden":602},[601],[572,4373,4375,4378,4381,4384],{"className":4374},[606],[572,4376],{"className":4377,"style":3989},[610],[572,4379,1620],{"className":4380,"style":1651},[888,1649,1650],[572,4382],{"className":4383,"style":892},[666],[572,4385,4387,4390,4449],{"className":4386},[615],[572,4388],{"className":4389},[1265,1387],[572,4391,4393],{"className":4392},[1321],[572,4394,4396,4441],{"className":4395},[904,938],[572,4397,4399,4438],{"className":4398},[908],[572,4400,4402,4416,4424],{"className":4401,"style":1400},[912],[572,4403,4404,4407],{"style":2160},[572,4405],{"className":4406,"style":1407},[920],[572,4408,4410],{"className":4409},[925,926,992,928],[572,4411,4413],{"className":4412},[615,928],[572,4414,593],{"className":4415},[615,616,928],[572,4417,4418,4421],{"style":1566},[572,4419],{"className":4420,"style":1407},[920],[572,4422],{"className":4423,"style":1574},[1573],[572,4425,4426,4429],{"style":1577},[572,4427],{"className":4428,"style":1407},[920],[572,4430,4432],{"className":4431},[925,926,992,928],[572,4433,4435],{"className":4434},[615,928],[572,4436,646],{"className":4437},[615,928],[572,4439,1000],{"className":4440},[999],[572,4442,4444],{"className":4443},[908],[572,4445,4447],{"className":4446,"style":2937},[912],[572,4448],{},[572,4450],{"className":4451},[1273,1387],[572,4453,4455,4479],{"className":4454},[575],[572,4456,4458],{"className":4457},[579],[581,4459,4460],{"xmlns":583},[585,4461,4462,4476],{},[588,4463,4464,4466],{},[640,4465,1620],{},[1321,4467,4468,4470],{},[644,4469,646],{},[1242,4471,4472,4474],{},[591,4473,593],{},[644,4475,2093],{},[595,4477,4478],{"encoding":597},"\\sum \\frac{1}{n^2}",[572,4480,4482],{"className":4481,"ariaHidden":602},[601],[572,4483,4485,4488,4491,4494],{"className":4484},[606],[572,4486],{"className":4487,"style":3989},[610],[572,4489,1620],{"className":4490,"style":1651},[888,1649,1650],[572,4492],{"className":4493,"style":892},[666],[572,4495,4497,4500,4586],{"className":4496},[615],[572,4498],{"className":4499},[1265,1387],[572,4501,4503],{"className":4502},[1321],[572,4504,4506,4578],{"className":4505},[904,938],[572,4507,4509,4575],{"className":4508},[908],[572,4510,4512,4553,4561],{"className":4511,"style":1400},[912],[572,4513,4514,4517],{"style":2160},[572,4515],{"className":4516,"style":1407},[920],[572,4518,4520],{"className":4519},[925,926,992,928],[572,4521,4523],{"className":4522},[615,928],[572,4524,4526,4529],{"className":4525},[615,928],[572,4527,593],{"className":4528},[615,616,928],[572,4530,4532],{"className":4531},[971],[572,4533,4535],{"className":4534},[904],[572,4536,4538],{"className":4537},[908],[572,4539,4542],{"className":4540,"style":4541},[912],"height:0.7463em;",[572,4543,4544,4547],{"style":2868},[572,4545],{"className":4546,"style":921},[920],[572,4548,4550],{"className":4549},[925,1457,927,928],[572,4551,2093],{"className":4552},[615,928],[572,4554,4555,4558],{"style":1566},[572,4556],{"className":4557,"style":1407},[920],[572,4559],{"className":4560,"style":1574},[1573],[572,4562,4563,4566],{"style":1577},[572,4564],{"className":4565,"style":1407},[920],[572,4567,4569],{"className":4568},[925,926,992,928],[572,4570,4572],{"className":4571},[615,928],[572,4573,646],{"className":4574},[615,928],[572,4576,1000],{"className":4577},[999],[572,4579,4581],{"className":4580},[908],[572,4582,4584],{"className":4583,"style":2937},[912],[572,4585],{},[572,4587],{"className":4588},[1273,1387]," ist ",[572,4591,4593,4610],{"className":4592},[575],[572,4594,4596],{"className":4595},[579],[581,4597,4598],{"xmlns":583},[585,4599,4600,4608],{},[588,4601,4602,4604,4606],{},[591,4603,638],{},[640,4605,792],{},[644,4607,646],{},[595,4609,797],{"encoding":597},[572,4611,4613,4631],{"className":4612,"ariaHidden":602},[601],[572,4614,4616,4619,4622,4625,4628],{"className":4615},[606],[572,4617],{"className":4618,"style":807},[610],[572,4620,638],{"className":4621},[615,616],[572,4623],{"className":4624,"style":667},[666],[572,4626,792],{"className":4627},[671],[572,4629],{"className":4630,"style":667},[666],[572,4632,4634,4637],{"className":4633},[606],[572,4635],{"className":4636,"style":681},[610],[572,4638,646],{"className":4639},[615],", die eine divergiert, die andere konvergiert.",[622,4642,4643,4644,689],{},"Den Betrag vergessen, z.B. bei alternierenden Gliedern ",[572,4645,4647,4678],{"className":4646},[575],[572,4648,4650],{"className":4649},[579],[581,4651,4652],{"xmlns":583},[585,4653,4654,4675],{},[588,4655,4656,4658,4660,4662,4668],{},[640,4657,1237],{"stretchy":1236},[640,4659,3814],{},[644,4661,646],{},[1242,4663,4664,4666],{},[640,4665,1246],{"stretchy":1236},[591,4667,593],{},[861,4669,4670,4673],{},[591,4671,4672],{},"b",[591,4674,593],{},[595,4676,4677],{"encoding":597},"(-1)^n b_n",[572,4679,4681],{"className":4680,"ariaHidden":602},[601],[572,4682,4684,4687,4690,4693,4696,4725],{"className":4683},[606],[572,4685],{"className":4686,"style":1261},[610],[572,4688,1237],{"className":4689},[1265],[572,4691,3814],{"className":4692},[615],[572,4694,646],{"className":4695},[615],[572,4697,4699,4702],{"className":4698},[1273],[572,4700,1246],{"className":4701},[1273],[572,4703,4705],{"className":4704},[971],[572,4706,4708],{"className":4707},[904],[572,4709,4711],{"className":4710},[908],[572,4712,4714],{"className":4713,"style":1289},[912],[572,4715,4716,4719],{"style":1292},[572,4717],{"className":4718,"style":988},[920],[572,4720,4722],{"className":4721},[925,926,992,928],[572,4723,593],{"className":4724},[615,616,928],[572,4726,4728,4731],{"className":4727},[615],[572,4729,4672],{"className":4730},[615,616],[572,4732,4734],{"className":4733},[971],[572,4735,4737,4757],{"className":4736},[904,938],[572,4738,4740,4754],{"className":4739},[908],[572,4741,4743],{"className":4742,"style":981},[912],[572,4744,4745,4748],{"style":984},[572,4746],{"className":4747,"style":988},[920],[572,4749,4751],{"className":4750},[925,926,992,928],[572,4752,593],{"className":4753},[615,616,928],[572,4755,1000],{"className":4756},[999],[572,4758,4760],{"className":4759},[908],[572,4761,4763],{"className":4762,"style":1007},[912],[572,4764],{},[622,4766,4767,4892,4893,689],{},[572,4768,4770,4792],{"className":4769},[575],[572,4771,4773],{"className":4772},[579],[581,4774,4775],{"xmlns":583},[585,4776,4777,4789],{},[588,4778,4779,4785,4787],{},[852,4780,4781,4783],{},[591,4782,593],{},[591,4784,593],{},[640,4786,1747],{},[644,4788,3778],{},[595,4790,4791],{"encoding":597},"\\sqrt[n]{n} \\to 0",[572,4793,4795,4883],{"className":4794,"ariaHidden":602},[601],[572,4796,4798,4801,4874,4877,4880],{"className":4797},[606],[572,4799],{"className":4800,"style":1762},[610],[572,4802,4804,4830],{"className":4803},[615,896],[572,4805,4807],{"className":4806},[900],[572,4808,4810],{"className":4809},[904],[572,4811,4813],{"className":4812},[908],[572,4814,4816],{"className":4815,"style":1778},[912],[572,4817,4818,4821],{"style":1781},[572,4819],{"className":4820,"style":921},[920],[572,4822,4824],{"className":4823},[925,926,927,928],[572,4825,4827],{"className":4826},[615,928],[572,4828,593],{"className":4829},[615,616,928],[572,4831,4833,4866],{"className":4832},[904,938],[572,4834,4836,4863],{"className":4835},[908],[572,4837,4839,4851],{"className":4838,"style":1803},[912],[572,4840,4842,4845],{"className":4841,"style":1807},[949],[572,4843],{"className":4844,"style":1407},[920],[572,4846,4848],{"className":4847,"style":1814},[615],[572,4849,593],{"className":4850},[615,616],[572,4852,4853,4856],{"style":1820},[572,4854],{"className":4855,"style":1407},[920],[572,4857,4859],{"className":4858,"style":1827},[1022],[1025,4860,4861],{"xmlns":1027,"width":1028,"height":1830,"viewBox":1548,"preserveAspectRatio":1031},[1033,4862],{"d":1551},[572,4864,1000],{"className":4865},[999],[572,4867,4869],{"className":4868},[908],[572,4870,4872],{"className":4871,"style":1842},[912],[572,4873],{},[572,4875],{"className":4876,"style":667},[666],[572,4878,1747],{"className":4879},[671],[572,4881],{"className":4882,"style":667},[666],[572,4884,4886,4889],{"className":4885},[606],[572,4887],{"className":4888,"style":681},[610],[572,4890,3778],{"className":4891},[615]," annehmen. Richtig ist 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für alle ",[572,5199,5201,5214],{"className":5200},[575],[572,5202,5204],{"className":5203},[579],[581,5205,5206],{"xmlns":583},[585,5207,5208,5212],{},[588,5209,5210],{},[591,5211,593],{},[595,5213,593],{"encoding":597},[572,5215,5217],{"className":5216,"ariaHidden":602},[601],[572,5218,5220,5223],{"className":5219},[606],[572,5221],{"className":5222,"style":611},[610],[572,5224,593],{"className":5225},[615,616]," auf Konvergenz schließen. Der Limes superior muss echt kleiner als ",[572,5228,5230,5243],{"className":5229},[575],[572,5231,5233],{"className":5232},[579],[581,5234,5235],{"xmlns":583},[585,5236,5237,5241],{},[588,5238,5239],{},[644,5240,646],{},[595,5242,646],{"encoding":597},[572,5244,5246],{"className":5245,"ariaHidden":602},[601],[572,5247,5249,5252],{"className":5248},[606],[572,5250],{"className":5251,"style":681},[610],[572,5253,646],{"className":5254},[615]," sein.",{"title":5257,"searchDepth":5258,"depth":5258,"links":5259},"",2,[5260,5261,5262],{"id":561,"depth":5258,"text":562},{"id":2061,"depth":5258,"text":2062},{"id":4288,"depth":5258,"text":4289},[5264,5267,5270,5274,5277,5280,5283,5287,5290],{"lhs":5265,"rhs":5266},"((n\u002F(2*n + 1))^n)^(1\u002Fn)","n\u002F(2*n + 1)",{"lhs":5268,"rhs":5269},"nthRoot((7\u002F15)^7, 7)","7\u002F15",{"lhs":5266,"rhs":5271,"where":5272},"100\u002F201",{"n":5273},100,{"lhs":5275,"rhs":5276},"(n^2\u002F3^n)^(1\u002Fn)","n^(2\u002Fn)\u002F3",{"lhs":5278,"rhs":5279},"round(1000^(2\u002F1000)\u002F3, 4)","0.338",{"lhs":5281,"rhs":5282},"round(sum((1:40).^2 .\u002F 3.^(1:40)), 9)","1.5",{"lhs":5284,"rhs":2093,"where":5285},"2^(-(n + 1) + (-1)^(n + 1)) \u002F 2^(-n + (-1)^n)",{"n":5286},1,{"lhs":5284,"rhs":5288,"where":5289},"1\u002F8",{"n":5258},{"lhs":5291,"rhs":5292,"where":5293},"(2^(-n + (-1)^n))^(1\u002Fn)","2^(-1 + 1\u002Fn)",{"n":5294},10,null,"md","root-test","L = \\limsup_{n \\to \\infty} \\sqrt[n]{|a_n|} \u003C 1 \\;\\Rightarrow\\; \\sum_{n=1}^{\\infty} a_n \\text{ konvergiert absolut}","\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>\u003Cmi>L\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmunder>\u003Cmrow>\u003Cmi mathvariant=\"normal\">lim sup\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>→\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmunder>\u003Cmroot>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmroot>\u003Cmo><\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⇒\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\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>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmtext> konvergiert absolut\u003C\u002Fmtext>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">L = \\limsup_{n \\to \\infty} \\sqrt[n]{|a_n|} < 1 \\;\\Rightarrow\\; \\sum_{n=1}^{\\infty} a_n \\text{ konvergiert absolut}\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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">L\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\" 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style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">⇒\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.9185em;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\" 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class=\"mord\"> konvergiert absolut\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fwurzelkriterium",[],[5306,5307,5308],"ratio-test","geometric-series","harmonic-series",{"title":548,"description":5257},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fwurzelkriterium","Ist der Limes superior von ⁿ√|aₙ| kleiner als 1, konvergiert die Reihe absolut; ist er größer als 1, divergiert sie.",[5313,5314,5315,5316],"konvergenzkriterium","reihe","konvergenz","absolute konvergenz",[5318,5321,5324],{"symbol":1170,"meaning":5319,"symbolHtml":5320},"n-tes Glied der Reihe","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation 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