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ab einem Index und divergiert ",[578,1097,1099,1119],{"className":1098},[581],[578,1100,1102],{"className":1101},[585],[587,1103,1104],{"xmlns":589},[591,1105,1106,1116],{},[594,1107,1108,1110],{},[613,1109,780],{},[602,1111,1112,1114],{},[597,1113,956],{},[597,1115,609],{},[624,1117,1118],{"encoding":626},"\\sum 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",[578,1176,1178,1197],{"className":1177},[581],[578,1179,1181],{"className":1180},[585],[587,1182,1183],{"xmlns":589},[591,1184,1185,1195],{},[594,1186,1187,1189],{},[613,1188,780],{},[602,1190,1191,1193],{},[597,1192,606],{},[597,1194,609],{},[624,1196,873],{"encoding":626},[578,1198,1200],{"className":1199,"ariaHidden":632},[631],[578,1201,1203,1206,1209,1212],{"className":1202},[636],[578,1204],{"className":1205,"style":641},[640],[578,1207,780],{"className":1208,"style":805},[802,803,804],[578,1210],{"className":1211,"style":809},[709],[578,1213,1215,1218],{"className":1214},[645],[578,1216,606],{"className":1217},[645,652],[578,1219,1221],{"className":1220},[656],[578,1222,1224,1244],{"className":1223},[660,661],[578,1225,1227,1241],{"className":1226},[665],[578,1228,1230],{"className":1229,"style":670},[669],[578,1231,1232,1235],{"style":673},[578,1233],{"className":1234,"style":678},[677],[578,1236,1238],{"className":1237},[682,683,684,685],[578,1239,609],{"className":1240},[645,652,685],[578,1242,693],{"className":1243},[692],[578,1245,1247],{"className":1246},[665],[578,1248,1250],{"className":1249,"style":700},[669],[578,1251],{},".",[564,1254,1255,1256,1328,1329,1393,1394,1548,1549,1602],{},"Als Vergleichsreihen dienen vor allem die geometrische Reihe ",[578,1257,1259,1281],{"className":1258},[581],[578,1260,1262],{"className":1261},[585],[587,1263,1264],{"xmlns":589},[591,1265,1266,1278],{},[594,1267,1268,1270],{},[613,1269,780],{},[1271,1272,1273,1276],"msup",{},[597,1274,1275],{},"q",[597,1277,609],{},[624,1279,1280],{"encoding":626},"\\sum q^n",[578,1282,1284],{"className":1283,"ariaHidden":632},[631],[578,1285,1287,1290,1293,1296],{"className":1286},[636],[578,1288],{"className":1289,"style":641},[640],[578,1291,780],{"className":1292,"style":805},[802,803,804],[578,1294],{"className":1295,"style":809},[709],[578,1297,1299,1303],{"className":1298},[645],[578,1300,1275],{"className":1301,"style":1302},[645,652],"margin-right:0.0359em;",[578,1304,1306],{"className":1305},[656],[578,1307,1309],{"className":1308},[660],[578,1310,1312],{"className":1311},[665],[578,1313,1316],{"className":1314,"style":1315},[669],"height:0.6644em;",[578,1317,1319,1322],{"style":1318},"top:-3.063em;margin-right:0.05em;",[578,1320],{"className":1321,"style":678},[677],[578,1323,1325],{"className":1324},[682,683,684,685],[578,1326,609],{"className":1327},[645,652,685]," (konvergent für ",[578,1330,1332,1356],{"className":1331},[581],[578,1333,1335],{"className":1334},[585],[587,1336,1337],{"xmlns":589},[591,1338,1339,1353],{},[594,1340,1341,1343,1345,1347,1350],{},[597,1342,600],{"mathvariant":599},[597,1344,1275],{},[597,1346,600],{"mathvariant":599},[613,1348,1349],{},"\u003C",[947,1351,1352],{},"1",[624,1354,1355],{"encoding":626},"|q| \u003C 1",[578,1357,1359,1383],{"className":1358,"ariaHidden":632},[631],[578,1360,1362,1365,1368,1371,1374,1377,1380],{"className":1361},[636],[578,1363],{"className":1364,"style":641},[640],[578,1366,600],{"className":1367},[645],[578,1369,1275],{"className":1370,"style":1302},[645,652],[578,1372,600],{"className":1373},[645],[578,1375],{"className":1376,"style":710},[709],[578,1378,1349],{"className":1379},[714],[578,1381],{"className":1382,"style":710},[709],[578,1384,1386,1390],{"className":1385},[636],[578,1387],{"className":1388,"style":1389},[640],"height:0.6444em;",[578,1391,1352],{"className":1392},[645],") und die Reihen ",[578,1395,1397,1422],{"className":1396},[581],[578,1398,1400],{"className":1399},[585],[587,1401,1402],{"xmlns":589},[591,1403,1404,1419],{},[594,1405,1406,1408],{},[613,1407,780],{},[1409,1410,1411,1413],"mfrac",{},[947,1412,1352],{},[1271,1414,1415,1417],{},[597,1416,609],{},[597,1418,564],{},[624,1420,1421],{"encoding":626},"\\sum \\frac{1}{n^p}",[578,1423,1425],{"className":1424,"ariaHidden":632},[631],[578,1426,1428,1432,1435,1438],{"className":1427},[636],[578,1429],{"className":1430,"style":1431},[640],"height:1.1901em;vertical-align:-0.345em;",[578,1433,780],{"className":1434,"style":805},[802,803,804],[578,1436],{"className":1437,"style":809},[709],[578,1439,1441,1446,1544],{"className":1440},[645],[578,1442],{"className":1443},[1444,1445],"mopen","nulldelimiter",[578,1447,1449],{"className":1448},[1409],[578,1450,1452,1535],{"className":1451},[660,661],[578,1453,1455,1532],{"className":1454},[665],[578,1456,1459,1506,1517],{"className":1457,"style":1458},[669],"height:0.8451em;",[578,1460,1462,1466],{"style":1461},"top:-2.655em;",[578,1463],{"className":1464,"style":1465},[677],"height:3em;",[578,1467,1469],{"className":1468},[682,683,684,685],[578,1470,1472],{"className":1471},[645,685],[578,1473,1475,1478],{"className":1474},[645,685],[578,1476,609],{"className":1477},[645,652,685],[578,1479,1481],{"className":1480},[656],[578,1482,1484],{"className":1483},[660],[578,1485,1487],{"className":1486},[665],[578,1488,1491],{"className":1489,"style":1490},[669],"height:0.5935em;",[578,1492,1494,1498],{"style":1493},"top:-2.786em;margin-right:0.0714em;",[578,1495],{"className":1496,"style":1497},[677],"height:2.5em;",[578,1499,1503],{"className":1500},[682,1501,1502,685],"reset-size3","size1",[578,1504,564],{"className":1505},[645,652,685],[578,1507,1509,1512],{"style":1508},"top:-3.23em;",[578,1510],{"className":1511,"style":1465},[677],[578,1513],{"className":1514,"style":1516},[1515],"frac-line","border-bottom-width:0.04em;",[578,1518,1520,1523],{"style":1519},"top:-3.394em;",[578,1521],{"className":1522,"style":1465},[677],[578,1524,1526],{"className":1525},[682,683,684,685],[578,1527,1529],{"className":1528},[645,685],[578,1530,1352],{"className":1531},[645,685],[578,1533,693],{"className":1534},[692],[578,1536,1538],{"className":1537},[665],[578,1539,1542],{"className":1540,"style":1541},[669],"height:0.345em;",[578,1543],{},[578,1545],{"className":1546},[1547,1445],"mclose"," (konvergent genau für ",[578,1550,1552,1571],{"className":1551},[581],[578,1553,1555],{"className":1554},[585],[587,1556,1557],{"xmlns":589},[591,1558,1559,1568],{},[594,1560,1561,1563,1566],{},[597,1562,564],{},[613,1564,1565],{},">",[947,1567,1352],{},[624,1569,1570],{"encoding":626},"p > 1",[578,1572,1574,1593],{"className":1573,"ariaHidden":632},[631],[578,1575,1577,1581,1584,1587,1590],{"className":1576},[636],[578,1578],{"className":1579,"style":1580},[640],"height:0.7335em;vertical-align:-0.1944em;",[578,1582,564],{"className":1583},[645,652],[578,1585],{"className":1586,"style":710},[709],[578,1588,1565],{"className":1589},[714],[578,1591],{"className":1592,"style":710},[709],[578,1594,1596,1599],{"className":1595},[636],[578,1597],{"className":1598,"style":1389},[640],[578,1600,1352],{"className":1601},[645],").",[564,1604,1605,1606,1609,1610,1759,1760,1971,1972,2048],{},"Eine bequeme Variante ist das ",[574,1607,1608],{},"Grenzwertkriterium",": Sind ",[578,1611,1613,1644],{"className":1612},[581],[578,1614,1616],{"className":1615},[585],[587,1617,1618],{"xmlns":589},[591,1619,1620,1641],{},[594,1621,1622,1628,1631,1637,1639],{},[602,1623,1624,1626],{},[597,1625,606],{},[597,1627,609],{},[613,1629,1630],{"separator":632},",",[602,1632,1633,1635],{},[597,1634,620],{},[597,1636,609],{},[613,1638,1565],{},[947,1640,949],{},[624,1642,1643],{"encoding":626},"a_n, b_n > 0",[578,1645,1647,1750],{"className":1646,"ariaHidden":632},[631],[578,1648,1650,1654,1694,1698,1701,1741,1744,1747],{"className":1649},[636],[578,1651],{"className":1652,"style":1653},[640],"height:0.8889em;vertical-align:-0.1944em;",[578,1655,1657,1660],{"className":1656},[645],[578,1658,606],{"className":1659},[645,652],[578,1661,1663],{"className":1662},[656],[578,1664,1666,1686],{"className":1665},[660,661],[578,1667,1669,1683],{"className":1668},[665],[578,1670,1672],{"className":1671,"style":670},[669],[578,1673,1674,1677],{"style":673},[578,1675],{"className":1676,"style":678},[677],[578,1678,1680],{"className":1679},[682,683,684,685],[578,1681,609],{"className":1682},[645,652,685],[578,1684,693],{"className":1685},[692],[578,1687,1689],{"className":1688},[665],[578,1690,1692],{"className":1691,"style":700},[669],[578,1693],{},[578,1695,1630],{"className":1696},[1697],"mpunct",[578,1699],{"className":1700,"style":809},[709],[578,1702,1704,1707],{"className":1703},[645],[578,1705,620],{"className":1706},[645,652],[578,1708,1710],{"className":1709},[656],[578,1711,1713,1733],{"className":1712},[660,661],[578,1714,1716,1730],{"className":1715},[665],[578,1717,1719],{"className":1718,"style":670},[669],[578,1720,1721,1724],{"style":673},[578,1722],{"className":1723,"style":678},[677],[578,1725,1727],{"className":1726},[682,683,684,685],[578,1728,609],{"className":1729},[645,652,685],[578,1731,693],{"className":1732},[692],[578,1734,1736],{"className":1735},[665],[578,1737,1739],{"className":1738,"style":700},[669],[578,1740],{},[578,1742],{"className":1743,"style":710},[709],[578,1745,1565],{"className":1746},[714],[578,1748],{"className":1749,"style":710},[709],[578,1751,1753,1756],{"className":1752},[636],[578,1754],{"className":1755,"style":1389},[640],[578,1757,949],{"className":1758},[645]," und gilt ",[578,1761,1763,1794],{"className":1762},[581],[578,1764,1766],{"className":1765},[585],[587,1767,1768],{"xmlns":589},[591,1769,1770,1791],{},[594,1771,1772,1786,1789],{},[1409,1773,1774,1780],{},[602,1775,1776,1778],{},[597,1777,606],{},[597,1779,609],{},[602,1781,1782,1784],{},[597,1783,620],{},[597,1785,609],{},[613,1787,1788],{},"→",[597,1790,956],{},[624,1792,1793],{"encoding":626},"\\frac{a_n}{b_n} \\to c",[578,1795,1797,1961],{"className":1796,"ariaHidden":632},[631],[578,1798,1800,1804,1952,1955,1958],{"className":1799},[636],[578,1801],{"className":1802,"style":1803},[640],"height:1.1566em;vertical-align:-0.4451em;",[578,1805,1807,1810,1949],{"className":1806},[645],[578,1808],{"className":1809},[1444,1445],[578,1811,1813],{"className":1812},[1409],[578,1814,1816,1940],{"className":1815},[660,661],[578,1817,1819,1937],{"className":1818},[665],[578,1820,1823,1877,1885],{"className":1821,"style":1822},[669],"height:0.7115em;",[578,1824,1825,1828],{"style":1461},[578,1826],{"className":1827,"style":1465},[677],[578,1829,1831],{"className":1830},[682,683,684,685],[578,1832,1834],{"className":1833},[645,685],[578,1835,1837,1840],{"className":1836},[645,685],[578,1838,620],{"className":1839},[645,652,685],[578,1841,1843],{"className":1842},[656],[578,1844,1846,1868],{"className":1845},[660,661],[578,1847,1849,1865],{"className":1848},[665],[578,1850,1853],{"className":1851,"style":1852},[669],"height:0.1645em;",[578,1854,1856,1859],{"style":1855},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[578,1857],{"className":1858,"style":1497},[677],[578,1860,1862],{"className":1861},[682,1501,1502,685],[578,1863,609],{"className":1864},[645,652,685],[578,1866,693],{"className":1867},[692],[578,1869,1871],{"className":1870},[665],[578,1872,1875],{"className":1873,"style":1874},[669],"height:0.143em;",[578,1876],{},[578,1878,1879,1882],{"style":1508},[578,1880],{"className":1881,"style":1465},[677],[578,1883],{"className":1884,"style":1516},[1515],[578,1886,1888,1891],{"style":1887},"top:-3.4101em;",[578,1889],{"className":1890,"style":1465},[677],[578,1892,1894],{"className":1893},[682,683,684,685],[578,1895,1897],{"className":1896},[645,685],[578,1898,1900,1903],{"className":1899},[645,685],[578,1901,606],{"className":1902},[645,652,685],[578,1904,1906],{"className":1905},[656],[578,1907,1909,1929],{"className":1908},[660,661],[578,1910,1912,1926],{"className":1911},[665],[578,1913,1915],{"className":1914,"style":1852},[669],[578,1916,1917,1920],{"style":1855},[578,1918],{"className":1919,"style":1497},[677],[578,1921,1923],{"className":1922},[682,1501,1502,685],[578,1924,609],{"className":1925},[645,652,685],[578,1927,693],{"className":1928},[692],[578,1930,1932],{"className":1931},[665],[578,1933,1935],{"className":1934,"style":1874},[669],[578,1936],{},[578,1938,693],{"className":1939},[692],[578,1941,1943],{"className":1942},[665],[578,1944,1947],{"className":1945,"style":1946},[669],"height:0.4451em;",[578,1948],{},[578,1950],{"className":1951},[1547,1445],[578,1953],{"className":1954,"style":710},[709],[578,1956,1788],{"className":1957},[714],[578,1959],{"className":1960,"style":710},[709],[578,1962,1964,1968],{"className":1963},[636],[578,1965],{"className":1966,"style":1967},[640],"height:0.4306em;",[578,1969,956],{"className":1970},[645,652]," mit ",[578,1973,1975,1998],{"className":1974},[581],[578,1976,1978],{"className":1977},[585],[587,1979,1980],{"xmlns":589},[591,1981,1982,1995],{},[594,1983,1984,1986,1988,1990,1992],{},[947,1985,949],{},[613,1987,1349],{},[597,1989,956],{},[613,1991,1349],{},[597,1993,1994],{"mathvariant":599},"∞",[624,1996,1997],{"encoding":626},"0 \u003C c \u003C \\infty",[578,1999,2001,2020,2039],{"className":2000,"ariaHidden":632},[631],[578,2002,2004,2008,2011,2014,2017],{"className":2003},[636],[578,2005],{"className":2006,"style":2007},[640],"height:0.6835em;vertical-align:-0.0391em;",[578,2009,949],{"className":2010},[645],[578,2012],{"className":2013,"style":710},[709],[578,2015,1349],{"className":2016},[714],[578,2018],{"className":2019,"style":710},[709],[578,2021,2023,2027,2030,2033,2036],{"className":2022},[636],[578,2024],{"className":2025,"style":2026},[640],"height:0.5782em;vertical-align:-0.0391em;",[578,2028,956],{"className":2029},[645,652],[578,2031],{"className":2032,"style":710},[709],[578,2034,1349],{"className":2035},[714],[578,2037],{"className":2038,"style":710},[709],[578,2040,2042,2045],{"className":2041},[636],[578,2043],{"className":2044,"style":1967},[640],[578,2046,1994],{"className":2047},[645],", dann konvergieren beide Reihen oder beide divergieren.",[559,2050,2052],{"id":2051},"beispiele","Beispiele",[564,2054,2055,2287,2288,2549,2550,2686,2687,3023,3024,3076,3077,3232,3233,1252],{},[578,2056,2058,2104],{"className":2057},[581],[578,2059,2061],{"className":2060},[585],[587,2062,2063],{"xmlns":589},[591,2064,2065,2101],{},[594,2066,2067,2083],{},[2068,2069,2070,2072,2081],"msubsup",{},[613,2071,780],{},[594,2073,2074,2076,2079],{},[597,2075,609],{},[613,2077,2078],{},"=",[947,2080,1352],{},[597,2082,1994],{"mathvariant":599},[1409,2084,2085,2087],{},[947,2086,1352],{},[594,2088,2089,2096,2099],{},[1271,2090,2091,2093],{},[597,2092,609],{},[947,2094,2095],{},"2",[613,2097,2098],{},"+",[597,2100,609],{},[624,2102,2103],{"encoding":626},"\\sum_{n=1}^{\\infty} \\frac{1}{n^2 + n}",[578,2105,2107],{"className":2106,"ariaHidden":632},[631],[578,2108,2110,2114,2181,2184],{"className":2109},[636],[578,2111],{"className":2112,"style":2113},[640],"height:1.2484em;vertical-align:-0.4033em;",[578,2115,2117,2120],{"className":2116},[802],[578,2118,780],{"className":2119,"style":805},[802,803,804],[578,2121,2123],{"className":2122},[656],[578,2124,2126,2172],{"className":2125},[660,661],[578,2127,2129,2169],{"className":2128},[665],[578,2130,2133,2154],{"className":2131,"style":2132},[669],"height:0.8043em;",[578,2134,2136,2139],{"style":2135},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[578,2137],{"className":2138,"style":678},[677],[578,2140,2142],{"className":2141},[682,683,684,685],[578,2143,2145,2148,2151],{"className":2144},[645,685],[578,2146,609],{"className":2147},[645,652,685],[578,2149,2078],{"className":2150},[714,685],[578,2152,1352],{"className":2153},[645,685],[578,2155,2157,2160],{"style":2156},"top:-3.2029em;margin-right:0.05em;",[578,2158],{"className":2159,"style":678},[677],[578,2161,2163],{"className":2162},[682,683,684,685],[578,2164,2166],{"className":2165},[645,685],[578,2167,1994],{"className":2168},[645,685],[578,2170,693],{"className":2171},[692],[578,2173,2175],{"className":2174},[665],[578,2176,2179],{"className":2177,"style":2178},[669],"height:0.2997em;",[578,2180],{},[578,2182],{"className":2183,"style":809},[709],[578,2185,2187,2190,2284],{"className":2186},[645],[578,2188],{"className":2189},[1444,1445],[578,2191,2193],{"className":2192},[1409],[578,2194,2196,2275],{"className":2195},[660,661],[578,2197,2199,2272],{"className":2198},[665],[578,2200,2202,2250,2258],{"className":2201,"style":1458},[669],[578,2203,2204,2207],{"style":1461},[578,2205],{"className":2206,"style":1465},[677],[578,2208,2210],{"className":2209},[682,683,684,685],[578,2211,2213,2243,2247],{"className":2212},[645,685],[578,2214,2216,2219],{"className":2215},[645,685],[578,2217,609],{"className":2218},[645,652,685],[578,2220,2222],{"className":2221},[656],[578,2223,2225],{"className":2224},[660],[578,2226,2228],{"className":2227},[665],[578,2229,2232],{"className":2230,"style":2231},[669],"height:0.7463em;",[578,2233,2234,2237],{"style":1493},[578,2235],{"className":2236,"style":1497},[677],[578,2238,2240],{"className":2239},[682,1501,1502,685],[578,2241,2095],{"className":2242},[645,685],[578,2244,2098],{"className":2245},[2246,685],"mbin",[578,2248,609],{"className":2249},[645,652,685],[578,2251,2252,2255],{"style":1508},[578,2253],{"className":2254,"style":1465},[677],[578,2256],{"className":2257,"style":1516},[1515],[578,2259,2260,2263],{"style":1519},[578,2261],{"className":2262,"style":1465},[677],[578,2264,2266],{"className":2265},[682,683,684,685],[578,2267,2269],{"className":2268},[645,685],[578,2270,1352],{"className":2271},[645,685],[578,2273,693],{"className":2274},[692],[578,2276,2278],{"className":2277},[665],[578,2279,2282],{"className":2280,"style":2281},[669],"height:0.4033em;",[578,2283],{},[578,2285],{"className":2286},[1547,1445],": Wegen ",[578,2289,2291,2331],{"className":2290},[581],[578,2292,2294],{"className":2293},[585],[587,2295,2296],{"xmlns":589},[591,2297,2298,2328],{},[594,2299,2300,2316,2318],{},[1409,2301,2302,2304],{},[947,2303,1352],{},[594,2305,2306,2312,2314],{},[1271,2307,2308,2310],{},[597,2309,609],{},[947,2311,2095],{},[613,2313,2098],{},[597,2315,609],{},[613,2317,615],{},[1409,2319,2320,2322],{},[947,2321,1352],{},[1271,2323,2324,2326],{},[597,2325,609],{},[947,2327,2095],{},[624,2329,2330],{"encoding":626},"\\frac{1}{n^2 + n} \\leq \\frac{1}{n^2}",[578,2332,2334,2449],{"className":2333,"ariaHidden":632},[631],[578,2335,2337,2340,2440,2443,2446],{"className":2336},[636],[578,2338],{"className":2339,"style":2113},[640],[578,2341,2343,2346,2437],{"className":2342},[645],[578,2344],{"className":2345},[1444,1445],[578,2347,2349],{"className":2348},[1409],[578,2350,2352,2429],{"className":2351},[660,661],[578,2353,2355,2426],{"className":2354},[665],[578,2356,2358,2404,2412],{"className":2357,"style":1458},[669],[578,2359,2360,2363],{"style":1461},[578,2361],{"className":2362,"style":1465},[677],[578,2364,2366],{"className":2365},[682,683,684,685],[578,2367,2369,2398,2401],{"className":2368},[645,685],[578,2370,2372,2375],{"className":2371},[645,685],[578,2373,609],{"className":2374},[645,652,685],[578,2376,2378],{"className":2377},[656],[578,2379,2381],{"className":2380},[660],[578,2382,2384],{"className":2383},[665],[578,2385,2387],{"className":2386,"style":2231},[669],[578,2388,2389,2392],{"style":1493},[578,2390],{"className":2391,"style":1497},[677],[578,2393,2395],{"className":2394},[682,1501,1502,685],[578,2396,2095],{"className":2397},[645,685],[578,2399,2098],{"className":2400},[2246,685],[578,2402,609],{"className":2403},[645,652,685],[578,2405,2406,2409],{"style":1508},[578,2407],{"className":2408,"style":1465},[677],[578,2410],{"className":2411,"style":1516},[1515],[578,2413,2414,2417],{"style":1519},[578,2415],{"className":2416,"style":1465},[677],[578,2418,2420],{"className":2419},[682,683,684,685],[578,2421,2423],{"className":2422},[645,685],[578,2424,1352],{"className":2425},[645,685],[578,2427,693],{"className":2428},[692],[578,2430,2432],{"className":2431},[665],[578,2433,2435],{"className":2434,"style":2281},[669],[578,2436],{},[578,2438],{"className":2439},[1547,1445],[578,2441],{"className":2442,"style":710},[709],[578,2444,615],{"className":2445},[714],[578,2447],{"className":2448,"style":710},[709],[578,2450,2452,2455],{"className":2451},[636],[578,2453],{"className":2454,"style":1431},[640],[578,2456,2458,2461,2546],{"className":2457},[645],[578,2459],{"className":2460},[1444,1445],[578,2462,2464],{"className":2463},[1409],[578,2465,2467,2538],{"className":2466},[660,661],[578,2468,2470,2535],{"className":2469},[665],[578,2471,2473,2513,2521],{"className":2472,"style":1458},[669],[578,2474,2475,2478],{"style":1461},[578,2476],{"className":2477,"style":1465},[677],[578,2479,2481],{"className":2480},[682,683,684,685],[578,2482,2484],{"className":2483},[645,685],[578,2485,2487,2490],{"className":2486},[645,685],[578,2488,609],{"className":2489},[645,652,685],[578,2491,2493],{"className":2492},[656],[578,2494,2496],{"className":2495},[660],[578,2497,2499],{"className":2498},[665],[578,2500,2502],{"className":2501,"style":2231},[669],[578,2503,2504,2507],{"style":1493},[578,2505],{"className":2506,"style":1497},[677],[578,2508,2510],{"className":2509},[682,1501,1502,685],[578,2511,2095],{"className":2512},[645,685],[578,2514,2515,2518],{"style":1508},[578,2516],{"className":2517,"style":1465},[677],[578,2519],{"className":2520,"style":1516},[1515],[578,2522,2523,2526],{"style":1519},[578,2524],{"className":2525,"style":1465},[677],[578,2527,2529],{"className":2528},[682,683,684,685],[578,2530,2532],{"className":2531},[645,685],[578,2533,1352],{"className":2534},[645,685],[578,2536,693],{"className":2537},[692],[578,2539,2541],{"className":2540},[665],[578,2542,2544],{"className":2543,"style":1541},[669],[578,2545],{},[578,2547],{"className":2548},[1547,1445]," und der Konvergenz von ",[578,2551,2553,2577],{"className":2552},[581],[578,2554,2556],{"className":2555},[585],[587,2557,2558],{"xmlns":589},[591,2559,2560,2574],{},[594,2561,2562,2564],{},[613,2563,780],{},[1409,2565,2566,2568],{},[947,2567,1352],{},[1271,2569,2570,2572],{},[597,2571,609],{},[947,2573,2095],{},[624,2575,2576],{"encoding":626},"\\sum \\frac{1}{n^2}",[578,2578,2580],{"className":2579,"ariaHidden":632},[631],[578,2581,2583,2586,2589,2592],{"className":2582},[636],[578,2584],{"className":2585,"style":1431},[640],[578,2587,780],{"className":2588,"style":805},[802,803,804],[578,2590],{"className":2591,"style":809},[709],[578,2593,2595,2598,2683],{"className":2594},[645],[578,2596],{"className":2597},[1444,1445],[578,2599,2601],{"className":2600},[1409],[578,2602,2604,2675],{"className":2603},[660,661],[578,2605,2607,2672],{"className":2606},[665],[578,2608,2610,2650,2658],{"className":2609,"style":1458},[669],[578,2611,2612,2615],{"style":1461},[578,2613],{"className":2614,"style":1465},[677],[578,2616,2618],{"className":2617},[682,683,684,685],[578,2619,2621],{"className":2620},[645,685],[578,2622,2624,2627],{"className":2623},[645,685],[578,2625,609],{"className":2626},[645,652,685],[578,2628,2630],{"className":2629},[656],[578,2631,2633],{"className":2632},[660],[578,2634,2636],{"className":2635},[665],[578,2637,2639],{"className":2638,"style":2231},[669],[578,2640,2641,2644],{"style":1493},[578,2642],{"className":2643,"style":1497},[677],[578,2645,2647],{"className":2646},[682,1501,1502,685],[578,2648,2095],{"className":2649},[645,685],[578,2651,2652,2655],{"style":1508},[578,2653],{"className":2654,"style":1465},[677],[578,2656],{"className":2657,"style":1516},[1515],[578,2659,2660,2663],{"style":1519},[578,2661],{"className":2662,"style":1465},[677],[578,2664,2666],{"className":2665},[682,683,684,685],[578,2667,2669],{"className":2668},[645,685],[578,2670,1352],{"className":2671},[645,685],[578,2673,693],{"className":2674},[692],[578,2676,2678],{"className":2677},[665],[578,2679,2681],{"className":2680,"style":1541},[669],[578,2682],{},[578,2684],{"className":2685},[1547,1445]," konvergiert die Reihe. Ihren Wert liefert die Zerlegung ",[578,2688,2690,2741],{"className":2689},[581],[578,2691,2693],{"className":2692},[585],[587,2694,2695],{"xmlns":589},[591,2696,2697,2738],{},[594,2698,2699,2715,2717,2723,2726],{},[1409,2700,2701,2703],{},[947,2702,1352],{},[594,2704,2705,2711,2713],{},[1271,2706,2707,2709],{},[597,2708,609],{},[947,2710,2095],{},[613,2712,2098],{},[597,2714,609],{},[613,2716,2078],{},[1409,2718,2719,2721],{},[947,2720,1352],{},[597,2722,609],{},[613,2724,2725],{},"−",[1409,2727,2728,2730],{},[947,2729,1352],{},[594,2731,2732,2734,2736],{},[597,2733,609],{},[613,2735,2098],{},[947,2737,1352],{},[624,2739,2740],{"encoding":626},"\\frac{1}{n^2 + n} = \\frac{1}{n} - \\frac{1}{n + 1}",[578,2742,2744,2859,2943],{"className":2743,"ariaHidden":632},[631],[578,2745,2747,2750,2850,2853,2856],{"className":2746},[636],[578,2748],{"className":2749,"style":2113},[640],[578,2751,2753,2756,2847],{"className":2752},[645],[578,2754],{"className":2755},[1444,1445],[578,2757,2759],{"className":2758},[1409],[578,2760,2762,2839],{"className":2761},[660,661],[578,2763,2765,2836],{"className":2764},[665],[578,2766,2768,2814,2822],{"className":2767,"style":1458},[669],[578,2769,2770,2773],{"style":1461},[578,2771],{"className":2772,"style":1465},[677],[578,2774,2776],{"className":2775},[682,683,684,685],[578,2777,2779,2808,2811],{"className":2778},[645,685],[578,2780,2782,2785],{"className":2781},[645,685],[578,2783,609],{"className":2784},[645,652,685],[578,2786,2788],{"className":2787},[656],[578,2789,2791],{"className":2790},[660],[578,2792,2794],{"className":2793},[665],[578,2795,2797],{"className":2796,"style":2231},[669],[578,2798,2799,2802],{"style":1493},[578,2800],{"className":2801,"style":1497},[677],[578,2803,2805],{"className":2804},[682,1501,1502,685],[578,2806,2095],{"className":2807},[645,685],[578,2809,2098],{"className":2810},[2246,685],[578,2812,609],{"className":2813},[645,652,685],[578,2815,2816,2819],{"style":1508},[578,2817],{"className":2818,"style":1465},[677],[578,2820],{"className":2821,"style":1516},[1515],[578,2823,2824,2827],{"style":1519},[578,2825],{"className":2826,"style":1465},[677],[578,2828,2830],{"className":2829},[682,683,684,685],[578,2831,2833],{"className":2832},[645,685],[578,2834,1352],{"className":2835},[645,685],[578,2837,693],{"className":2838},[692],[578,2840,2842],{"className":2841},[665],[578,2843,2845],{"className":2844,"style":2281},[669],[578,2846],{},[578,2848],{"className":2849},[1547,1445],[578,2851],{"className":2852,"style":710},[709],[578,2854,2078],{"className":2855},[714],[578,2857],{"className":2858,"style":710},[709],[578,2860,2862,2865,2933,2937,2940],{"className":2861},[636],[578,2863],{"className":2864,"style":1431},[640],[578,2866,2868,2871,2930],{"className":2867},[645],[578,2869],{"className":2870},[1444,1445],[578,2872,2874],{"className":2873},[1409],[578,2875,2877,2922],{"className":2876},[660,661],[578,2878,2880,2919],{"className":2879},[665],[578,2881,2883,2897,2905],{"className":2882,"style":1458},[669],[578,2884,2885,2888],{"style":1461},[578,2886],{"className":2887,"style":1465},[677],[578,2889,2891],{"className":2890},[682,683,684,685],[578,2892,2894],{"className":2893},[645,685],[578,2895,609],{"className":2896},[645,652,685],[578,2898,2899,2902],{"style":1508},[578,2900],{"className":2901,"style":1465},[677],[578,2903],{"className":2904,"style":1516},[1515],[578,2906,2907,2910],{"style":1519},[578,2908],{"className":2909,"style":1465},[677],[578,2911,2913],{"className":2912},[682,683,684,685],[578,2914,2916],{"className":2915},[645,685],[578,2917,1352],{"className":2918},[645,685],[578,2920,693],{"className":2921},[692],[578,2923,2925],{"className":2924},[665],[578,2926,2928],{"className":2927,"style":1541},[669],[578,2929],{},[578,2931],{"className":2932},[1547,1445],[578,2934],{"className":2935,"style":2936},[709],"margin-right:0.2222em;",[578,2938,2725],{"className":2939},[2246],[578,2941],{"className":2942,"style":2936},[709],[578,2944,2946,2949],{"className":2945},[636],[578,2947],{"className":2948,"style":2113},[640],[578,2950,2952,2955,3020],{"className":2951},[645],[578,2953],{"className":2954},[1444,1445],[578,2956,2958],{"className":2957},[1409],[578,2959,2961,3012],{"className":2960},[660,661],[578,2962,2964,3009],{"className":2963},[665],[578,2965,2967,2987,2995],{"className":2966,"style":1458},[669],[578,2968,2969,2972],{"style":1461},[578,2970],{"className":2971,"style":1465},[677],[578,2973,2975],{"className":2974},[682,683,684,685],[578,2976,2978,2981,2984],{"className":2977},[645,685],[578,2979,609],{"className":2980},[645,652,685],[578,2982,2098],{"className":2983},[2246,685],[578,2985,1352],{"className":2986},[645,685],[578,2988,2989,2992],{"style":1508},[578,2990],{"className":2991,"style":1465},[677],[578,2993],{"className":2994,"style":1516},[1515],[578,2996,2997,3000],{"style":1519},[578,2998],{"className":2999,"style":1465},[677],[578,3001,3003],{"className":3002},[682,683,684,685],[578,3004,3006],{"className":3005},[645,685],[578,3007,1352],{"className":3008},[645,685],[578,3010,693],{"className":3011},[692],[578,3013,3015],{"className":3014},[665],[578,3016,3018],{"className":3017,"style":2281},[669],[578,3019],{},[578,3021],{"className":3022},[1547,1445],": Die Teilsumme bis ",[578,3025,3027,3046],{"className":3026},[581],[578,3028,3030],{"className":3029},[585],[587,3031,3032],{"xmlns":589},[591,3033,3034,3043],{},[594,3035,3036,3038,3040],{},[597,3037,609],{},[613,3039,2078],{},[947,3041,3042],{},"99",[624,3044,3045],{"encoding":626},"n = 99",[578,3047,3049,3067],{"className":3048,"ariaHidden":632},[631],[578,3050,3052,3055,3058,3061,3064],{"className":3051},[636],[578,3053],{"className":3054,"style":1967},[640],[578,3056,609],{"className":3057},[645,652],[578,3059],{"className":3060,"style":710},[709],[578,3062,2078],{"className":3063},[714],[578,3065],{"className":3066,"style":710},[709],[578,3068,3070,3073],{"className":3069},[636],[578,3071],{"className":3072,"style":1389},[640],[578,3074,3042],{"className":3075},[645]," ist ",[578,3078,3080,3108],{"className":3079},[581],[578,3081,3083],{"className":3082},[585],[587,3084,3085],{"xmlns":589},[591,3086,3087,3105],{},[594,3088,3089,3091,3093,3100,3102],{},[947,3090,1352],{},[613,3092,2725],{},[1409,3094,3095,3097],{},[947,3096,1352],{},[947,3098,3099],{},"100",[613,3101,2078],{},[947,3103,3104],{},"0,99",[624,3106,3107],{"encoding":626},"1 - \\frac{1}{100} = 0{,}99",[578,3109,3111,3130,3213],{"className":3110,"ariaHidden":632},[631],[578,3112,3114,3118,3121,3124,3127],{"className":3113},[636],[578,3115],{"className":3116,"style":3117},[640],"height:0.7278em;vertical-align:-0.0833em;",[578,3119,1352],{"className":3120},[645],[578,3122],{"className":3123,"style":2936},[709],[578,3125,2725],{"className":3126},[2246],[578,3128],{"className":3129,"style":2936},[709],[578,3131,3133,3136,3204,3207,3210],{"className":3132},[636],[578,3134],{"className":3135,"style":1431},[640],[578,3137,3139,3142,3201],{"className":3138},[645],[578,3140],{"className":3141},[1444,1445],[578,3143,3145],{"className":3144},[1409],[578,3146,3148,3193],{"className":3147},[660,661],[578,3149,3151,3190],{"className":3150},[665],[578,3152,3154,3168,3176],{"className":3153,"style":1458},[669],[578,3155,3156,3159],{"style":1461},[578,3157],{"className":3158,"style":1465},[677],[578,3160,3162],{"className":3161},[682,683,684,685],[578,3163,3165],{"className":3164},[645,685],[578,3166,3099],{"className":3167},[645,685],[578,3169,3170,3173],{"style":1508},[578,3171],{"className":3172,"style":1465},[677],[578,3174],{"className":3175,"style":1516},[1515],[578,3177,3178,3181],{"style":1519},[578,3179],{"className":3180,"style":1465},[677],[578,3182,3184],{"className":3183},[682,683,684,685],[578,3185,3187],{"className":3186},[645,685],[578,3188,1352],{"className":3189},[645,685],[578,3191,693],{"className":3192},[692],[578,3194,3196],{"className":3195},[665],[578,3197,3199],{"className":3198,"style":1541},[669],[578,3200],{},[578,3202],{"className":3203},[1547,1445],[578,3205],{"className":3206,"style":710},[709],[578,3208,2078],{"className":3209},[714],[578,3211],{"className":3212,"style":710},[709],[578,3214,3216,3220,3223,3229],{"className":3215},[636],[578,3217],{"className":3218,"style":3219},[640],"height:0.8389em;vertical-align:-0.1944em;",[578,3221,949],{"className":3222},[645],[578,3224,3226],{"className":3225},[645],[578,3227,1630],{"className":3228},[1697],[578,3230,3042],{"className":3231},[645],", der Grenzwert ist 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\\frac{1}{2^n + n}",[578,3309,3311],{"className":3310,"ariaHidden":632},[631],[578,3312,3314,3317,3380,3383],{"className":3313},[636],[578,3315],{"className":3316,"style":2113},[640],[578,3318,3320,3323],{"className":3319},[802],[578,3321,780],{"className":3322,"style":805},[802,803,804],[578,3324,3326],{"className":3325},[656],[578,3327,3329,3372],{"className":3328},[660,661],[578,3330,3332,3369],{"className":3331},[665],[578,3333,3335,3355],{"className":3334,"style":2132},[669],[578,3336,3337,3340],{"style":2135},[578,3338],{"className":3339,"style":678},[677],[578,3341,3343],{"className":3342},[682,683,684,685],[578,3344,3346,3349,3352],{"className":3345},[645,685],[578,3347,609],{"className":3348},[645,652,685],[578,3350,2078],{"className":3351},[714,685],[578,3353,1352],{"className":3354},[645,685],[578,3356,3357,3360],{"style":2156},[578,3358],{"className":3359,"style":678},[677],[578,3361,3363],{"className":3362},[682,683,684,685],[578,3364,3366],{"className":3365},[645,685],[578,3367,1994],{"className":3368},[645,685],[578,3370,693],{"className":3371},[692],[578,3373,3375],{"className":3374},[665],[578,3376,3378],{"className":3377,"style":2178},[669],[578,3379],{},[578,3381],{"className":3382,"style":809},[709],[578,3384,3386,3389,3480],{"className":3385},[645],[578,3387],{"className":3388},[1444,1445],[578,3390,3392],{"className":3391},[1409],[578,3393,3395,3472],{"className":3394},[660,661],[578,3396,3398,3469],{"className":3397},[665],[578,3399,3401,3447,3455],{"className":3400,"style":1458},[669],[578,3402,3403,3406],{"style":1461},[578,3404],{"className":3405,"style":1465},[677],[578,3407,3409],{"className":3408},[682,683,684,685],[578,3410,3412,3441,3444],{"className":3411},[645,685],[578,3413,3415,3418],{"className":3414},[645,685],[578,3416,2095],{"className":3417},[645,685],[578,3419,3421],{"className":3420},[656],[578,3422,3424],{"className":3423},[660],[578,3425,3427],{"className":3426},[665],[578,3428,3430],{"className":3429,"style":1490},[669],[578,3431,3432,3435],{"style":1493},[578,3433],{"className":3434,"style":1497},[677],[578,3436,3438],{"className":3437},[682,1501,1502,685],[578,3439,609],{"className":3440},[645,652,685],[578,3442,2098],{"className":3443},[2246,685],[578,3445,609],{"className":3446},[645,652,685],[578,3448,3449,3452],{"style":1508},[578,3450],{"className":3451,"style":1465},[677],[578,3453],{"className":3454,"style":1516},[1515],[578,3456,3457,3460],{"style":1519},[578,3458],{"className":3459,"style":1465},[677],[578,3461,3463],{"className":3462},[682,683,684,685],[578,3464,3466],{"className":3465},[645,685],[578,3467,1352],{"className":3468},[645,685],[578,3470,693],{"className":3471},[692],[578,3473,3475],{"className":3474},[665],[578,3476,3478],{"className":3477,"style":2281},[669],[578,3479],{},[578,3481],{"className":3482},[1547,1445],": Es gilt ",[578,3485,3487,3535],{"className":3486},[581],[578,3488,3490],{"className":3489},[585],[587,3491,3492],{"xmlns":589},[591,3493,3494,3532],{},[594,3495,3496,3512,3514],{},[1409,3497,3498,3500],{},[947,3499,1352],{},[594,3501,3502,3508,3510],{},[1271,3503,3504,3506],{},[947,3505,2095],{},[597,3507,609],{},[613,3509,2098],{},[597,3511,609],{},[613,3513,615],{},[1271,3515,3516,3530],{},[594,3517,3518,3521,3527],{},[613,3519,3520],{"fence":632},"(",[1409,3522,3523,3525],{},[947,3524,1352],{},[947,3526,2095],{},[613,3528,3529],{"fence":632},")",[597,3531,609],{},[624,3533,3534],{"encoding":626},"\\frac{1}{2^n + n} \\leq \\left(\\frac{1}{2}\\right)^n",[578,3536,3538,3653],{"className":3537,"ariaHidden":632},[631],[578,3539,3541,3544,3644,3647,3650],{"className":3540},[636],[578,3542],{"className":3543,"style":2113},[640],[578,3545,3547,3550,3641],{"className":3546},[645],[578,3548],{"className":3549},[1444,1445],[578,3551,3553],{"className":3552},[1409],[578,3554,3556,3633],{"className":3555},[660,661],[578,3557,3559,3630],{"className":3558},[665],[578,3560,3562,3608,3616],{"className":3561,"style":1458},[669],[578,3563,3564,3567],{"style":1461},[578,3565],{"className":3566,"style":1465},[677],[578,3568,3570],{"className":3569},[682,683,684,685],[578,3571,3573,3602,3605],{"className":3572},[645,685],[578,3574,3576,3579],{"className":3575},[645,685],[578,3577,2095],{"className":3578},[645,685],[578,3580,3582],{"className":3581},[656],[578,3583,3585],{"className":3584},[660],[578,3586,3588],{"className":3587},[665],[578,3589,3591],{"className":3590,"style":1490},[669],[578,3592,3593,3596],{"style":1493},[578,3594],{"className":3595,"style":1497},[677],[578,3597,3599],{"className":3598},[682,1501,1502,685],[578,3600,609],{"className":3601},[645,652,685],[578,3603,2098],{"className":3604},[2246,685],[578,3606,609],{"className":3607},[645,652,685],[578,3609,3610,3613],{"style":1508},[578,3611],{"className":3612,"style":1465},[677],[578,3614],{"className":3615,"style":1516},[1515],[578,3617,3618,3621],{"style":1519},[578,3619],{"className":3620,"style":1465},[677],[578,3622,3624],{"className":3623},[682,683,684,685],[578,3625,3627],{"className":3626},[645,685],[578,3628,1352],{"className":3629},[645,685],[578,3631,693],{"className":3632},[692],[578,3634,3636],{"className":3635},[665],[578,3637,3639],{"className":3638,"style":2281},[669],[578,3640],{},[578,3642],{"className":3643},[1547,1445],[578,3645],{"className":3646,"style":710},[709],[578,3648,615],{"className":3649},[714],[578,3651],{"className":3652,"style":710},[709],[578,3654,3656,3660],{"className":3655},[636],[578,3657],{"className":3658,"style":3659},[640],"height:1.2543em;vertical-align:-0.35em;",[578,3661,3664,3750],{"className":3662},[3663],"minner",[578,3665,3667,3676,3744],{"className":3666},[3663],[578,3668,3672],{"className":3669,"style":3671},[1444,3670],"delimcenter","top:0em;",[578,3673,3520],{"className":3674},[3675,1502],"delimsizing",[578,3677,3679,3682,3741],{"className":3678},[645],[578,3680],{"className":3681},[1444,1445],[578,3683,3685],{"className":3684},[1409],[578,3686,3688,3733],{"className":3687},[660,661],[578,3689,3691,3730],{"className":3690},[665],[578,3692,3694,3708,3716],{"className":3693,"style":1458},[669],[578,3695,3696,3699],{"style":1461},[578,3697],{"className":3698,"style":1465},[677],[578,3700,3702],{"className":3701},[682,683,684,685],[578,3703,3705],{"className":3704},[645,685],[578,3706,2095],{"className":3707},[645,685],[578,3709,3710,3713],{"style":1508},[578,3711],{"className":3712,"style":1465},[677],[578,3714],{"className":3715,"style":1516},[1515],[578,3717,3718,3721],{"style":1519},[578,3719],{"className":3720,"style":1465},[677],[578,3722,3724],{"className":3723},[682,683,684,685],[578,3725,3727],{"className":3726},[645,685],[578,3728,1352],{"className":3729},[645,685],[578,3731,693],{"className":3732},[692],[578,3734,3736],{"className":3735},[665],[578,3737,3739],{"className":3738,"style":1541},[669],[578,3740],{},[578,3742],{"className":3743},[1547,1445],[578,3745,3747],{"className":3746,"style":3671},[1547,3670],[578,3748,3529],{"className":3749},[3675,1502],[578,3751,3753],{"className":3752},[656],[578,3754,3756],{"className":3755},[660],[578,3757,3759],{"className":3758},[665],[578,3760,3763],{"className":3761,"style":3762},[669],"height:0.9043em;",[578,3764,3766,3769],{"style":3765},"top:-3.3029em;margin-right:0.05em;",[578,3767],{"className":3768,"style":678},[677],[578,3770,3772],{"className":3771},[682,683,684,685],[578,3773,609],{"className":3774},[645,652,685],". Die geometrische Reihe mit ",[578,3777,3779,3801],{"className":3778},[581],[578,3780,3782],{"className":3781},[585],[587,3783,3784],{"xmlns":589},[591,3785,3786,3798],{},[594,3787,3788,3790,3792],{},[597,3789,1275],{},[613,3791,2078],{},[1409,3793,3794,3796],{},[947,3795,1352],{},[947,3797,2095],{},[624,3799,3800],{"encoding":626},"q = \\frac{1}{2}",[578,3802,3804,3823],{"className":3803,"ariaHidden":632},[631],[578,3805,3807,3811,3814,3817,3820],{"className":3806},[636],[578,3808],{"className":3809,"style":3810},[640],"height:0.625em;vertical-align:-0.1944em;",[578,3812,1275],{"className":3813,"style":1302},[645,652],[578,3815],{"className":3816,"style":710},[709],[578,3818,2078],{"className":3819},[714],[578,3821],{"className":3822,"style":710},[709],[578,3824,3826,3829],{"className":3825},[636],[578,3827],{"className":3828,"style":1431},[640],[578,3830,3832,3835,3894],{"className":3831},[645],[578,3833],{"className":3834},[1444,1445],[578,3836,3838],{"className":3837},[1409],[578,3839,3841,3886],{"className":3840},[660,661],[578,3842,3844,3883],{"className":3843},[665],[578,3845,3847,3861,3869],{"className":3846,"style":1458},[669],[578,3848,3849,3852],{"style":1461},[578,3850],{"className":3851,"style":1465},[677],[578,3853,3855],{"className":3854},[682,683,684,685],[578,3856,3858],{"className":3857},[645,685],[578,3859,2095],{"className":3860},[645,685],[578,3862,3863,3866],{"style":1508},[578,3864],{"className":3865,"style":1465},[677],[578,3867],{"className":3868,"style":1516},[1515],[578,3870,3871,3874],{"style":1519},[578,3872],{"className":3873,"style":1465},[677],[578,3875,3877],{"className":3876},[682,683,684,685],[578,3878,3880],{"className":3879},[645,685],[578,3881,1352],{"className":3882},[645,685],[578,3884,693],{"className":3885},[692],[578,3887,3889],{"className":3888},[665],[578,3890,3892],{"className":3891,"style":1541},[669],[578,3893],{},[578,3895],{"className":3896},[1547,1445]," hat den Wert ",[578,3899,3901,3914],{"className":3900},[581],[578,3902,3904],{"className":3903},[585],[587,3905,3906],{"xmlns":589},[591,3907,3908,3912],{},[594,3909,3910],{},[947,3911,1352],{},[624,3913,1352],{"encoding":626},[578,3915,3917],{"className":3916,"ariaHidden":632},[631],[578,3918,3920,3923],{"className":3919},[636],[578,3921],{"className":3922,"style":1389},[640],[578,3924,1352],{"className":3925},[645],", also konvergiert die Reihe mit einem Wert kleiner als ",[578,3928,3930,3943],{"className":3929},[581],[578,3931,3933],{"className":3932},[585],[587,3934,3935],{"xmlns":589},[591,3936,3937,3941],{},[594,3938,3939],{},[947,3940,1352],{},[624,3942,1352],{"encoding":626},[578,3944,3946],{"className":3945,"ariaHidden":632},[631],[578,3947,3949,3952],{"className":3948},[636],[578,3950],{"className":3951,"style":1389},[640],[578,3953,1352],{"className":3954},[645]," (er liegt bei etwa 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0 400000 1080","xMinYMin slice",[4191,4192],"path",{"d":4193},"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 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\\geq 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ist die harmonische Reihe eine divergente Minorante. Die Teilsummen bis ",[578,4481,4483,4496],{"className":4482},[581],[578,4484,4486],{"className":4485},[585],[587,4487,4488],{"xmlns":589},[591,4489,4490,4494],{},[594,4491,4492],{},[947,4493,3099],{},[624,4495,3099],{"encoding":626},[578,4497,4499],{"className":4498,"ariaHidden":632},[631],[578,4500,4502,4505],{"className":4501},[636],[578,4503],{"className":4504,"style":1389},[640],[578,4506,3099],{"className":4507},[645]," sind etwa ",[578,4510,4512,4527],{"className":4511},[581],[578,4513,4515],{"className":4514},[585],[587,4516,4517],{"xmlns":589},[591,4518,4519,4524],{},[594,4520,4521],{},[947,4522,4523],{},"18,59",[624,4525,4526],{"encoding":626},"18{,}59",[578,4528,4530],{"className":4529,"ariaHidden":632},[631],[578,4531,4533,4536,4540,4546],{"className":4532},[636],[578,4534],{"className":4535,"style":3219},[640],[578,4537,4539],{"className":4538},[645],"18",[578,4541,4543],{"className":4542},[645],[578,4544,1630],{"className":4545},[1697],[578,4547,4549],{"className":4548},[645],"59"," gegenüber ",[578,4552,4554,4569],{"className":4553},[581],[578,4555,4557],{"className":4556},[585],[587,4558,4559],{"xmlns":589},[591,4560,4561,4566],{},[594,4562,4563],{},[947,4564,4565],{},"5,19",[624,4567,4568],{"encoding":626},"5{,}19",[578,4570,4572],{"className":4571,"ariaHidden":632},[631],[578,4573,4575,4578,4582,4588],{"className":4574},[636],[578,4576],{"className":4577,"style":3219},[640],[578,4579,4581],{"className":4580},[645],"5",[578,4583,4585],{"className":4584},[645],[578,4586,1630],{"className":4587},[1697],[578,4589,4591],{"className":4590},[645],"19"," bei der harmonischen Reihe.",[559,4594,4596],{"id":4595},"typische-fehler","Typische Fehler",[568,4598,4599,4826,4832,5061],{},[571,4600,4601,4602,4605,4606,4825],{},"Eine Reihe durch eine ",[574,4603,4604],{},"divergente"," Reihe nach oben abschätzen. ",[578,4607,4609,4639],{"className":4608},[581],[578,4610,4612],{"className":4611},[585],[587,4613,4614],{"xmlns":589},[591,4615,4616,4636],{},[594,4617,4618,4628,4630],{},[1409,4619,4620,4622],{},[947,4621,1352],{},[1271,4623,4624,4626],{},[597,4625,609],{},[947,4627,2095],{},[613,4629,615],{},[1409,4631,4632,4634],{},[947,4633,1352],{},[597,4635,609],{},[624,4637,4638],{"encoding":626},"\\frac{1}{n^2} \\leq \\frac{1}{n}",[578,4640,4642,4751],{"className":4641,"ariaHidden":632},[631],[578,4643,4645,4648,4742,4745,4748],{"className":4644},[636],[578,4646],{"className":4647,"style":1431},[640],[578,4649,4651,4654,4739],{"className":4650},[645],[578,4652],{"className":4653},[1444,1445],[578,4655,4657],{"className":4656},[1409],[578,4658,4660,4731],{"className":4659},[660,661],[578,4661,4663,4728],{"className":4662},[665],[578,4664,4666,4706,4714],{"className":4665,"style":1458},[669],[578,4667,4668,4671],{"style":1461},[578,4669],{"className":4670,"style":1465},[677],[578,4672,4674],{"className":4673},[682,683,684,685],[578,4675,4677],{"className":4676},[645,685],[578,4678,4680,4683],{"className":4679},[645,685],[578,4681,609],{"className":4682},[645,652,685],[578,4684,4686],{"className":4685},[656],[578,4687,4689],{"className":4688},[660],[578,4690,4692],{"className":4691},[665],[578,4693,4695],{"className":4694,"style":2231},[669],[578,4696,4697,4700],{"style":1493},[578,4698],{"className":4699,"style":1497},[677],[578,4701,4703],{"className":4702},[682,1501,1502,685],[578,4704,2095],{"className":4705},[645,685],[578,4707,4708,4711],{"style":1508},[578,4709],{"className":4710,"style":1465},[677],[578,4712],{"className":4713,"style":1516},[1515],[578,4715,4716,4719],{"style":1519},[578,4717],{"className":4718,"style":1465},[677],[578,4720,4722],{"className":4721},[682,683,684,685],[578,4723,4725],{"className":4724},[645,685],[578,4726,1352],{"className":4727},[645,685],[578,4729,693],{"className":4730},[692],[578,4732,4734],{"className":4733},[665],[578,4735,4737],{"className":4736,"style":1541},[669],[578,4738],{},[578,4740],{"className":4741},[1547,1445],[578,4743],{"className":4744,"style":710},[709],[578,4746,615],{"className":4747},[714],[578,4749],{"className":4750,"style":710},[709],[578,4752,4754,4757],{"className":4753},[636],[578,4755],{"className":4756,"style":1431},[640],[578,4758,4760,4763,4822],{"className":4759},[645],[578,4761],{"className":4762},[1444,1445],[578,4764,4766],{"className":4765},[1409],[578,4767,4769,4814],{"className":4768},[660,661],[578,4770,4772,4811],{"className":4771},[665],[578,4773,4775,4789,4797],{"className":4774,"style":1458},[669],[578,4776,4777,4780],{"style":1461},[578,4778],{"className":4779,"style":1465},[677],[578,4781,4783],{"className":4782},[682,683,684,685],[578,4784,4786],{"className":4785},[645,685],[578,4787,609],{"className":4788},[645,652,685],[578,4790,4791,4794],{"style":1508},[578,4792],{"className":4793,"style":1465},[677],[578,4795],{"className":4796,"style":1516},[1515],[578,4798,4799,4802],{"style":1519},[578,4800],{"className":4801,"style":1465},[677],[578,4803,4805],{"className":4804},[682,683,684,685],[578,4806,4808],{"className":4807},[645,685],[578,4809,1352],{"className":4810},[645,685],[578,4812,693],{"className":4813},[692],[578,4815,4817],{"className":4816},[665],[578,4818,4820],{"className":4819,"style":1541},[669],[578,4821],{},[578,4823],{"className":4824},[1547,1445]," stimmt, beweist aber gar nichts.",[571,4827,4601,4828,4831],{},[574,4829,4830],{},"konvergente"," Reihe nach unten abschätzen. Auch daraus folgt nichts.",[571,4833,4834,4835,4968,4969,1252],{},"Beim Minorantenkriterium negative Glieder zulassen. Die Abschätzung ",[578,4836,4838,4864],{"className":4837},[581],[578,4839,4841],{"className":4840},[585],[587,4842,4843],{"xmlns":589},[591,4844,4845,4861],{},[594,4846,4847,4853,4855],{},[602,4848,4849,4851],{},[597,4850,956],{},[597,4852,609],{},[613,4854,615],{},[602,4856,4857,4859],{},[597,4858,606],{},[597,4860,609],{},[624,4862,4863],{"encoding":626},"c_n \\leq a_n",[578,4865,4867,4922],{"className":4866,"ariaHidden":632},[631],[578,4868,4870,4873,4913,4916,4919],{"className":4869},[636],[578,4871],{"className":4872,"style":998},[640],[578,4874,4876,4879],{"className":4875},[645],[578,4877,956],{"className":4878},[645,652],[578,4880,4882],{"className":4881},[656],[578,4883,4885,4905],{"className":4884},[660,661],[578,4886,4888,4902],{"className":4887},[665],[578,4889,4891],{"className":4890,"style":670},[669],[578,4892,4893,4896],{"style":673},[578,4894],{"className":4895,"style":678},[677],[578,4897,4899],{"className":4898},[682,683,684,685],[578,4900,609],{"className":4901},[645,652,685],[578,4903,693],{"className":4904},[692],[578,4906,4908],{"className":4907},[665],[578,4909,4911],{"className":4910,"style":700},[669],[578,4912],{},[578,4914],{"className":4915,"style":710},[709],[578,4917,615],{"className":4918},[714],[578,4920],{"className":4921,"style":710},[709],[578,4923,4925,4928],{"className":4924},[636],[578,4926],{"className":4927,"style":1054},[640],[578,4929,4931,4934],{"className":4930},[645],[578,4932,606],{"className":4933},[645,652],[578,4935,4937],{"className":4936},[656],[578,4938,4940,4960],{"className":4939},[660,661],[578,4941,4943,4957],{"className":4942},[665],[578,4944,4946],{"className":4945,"style":670},[669],[578,4947,4948,4951],{"style":673},[578,4949],{"className":4950,"style":678},[677],[578,4952,4954],{"className":4953},[682,683,684,685],[578,4955,609],{"className":4956},[645,652,685],[578,4958,693],{"className":4959},[692],[578,4961,4963],{"className":4962},[665],[578,4964,4966],{"className":4965,"style":700},[669],[578,4967],{}," braucht ",[578,4970,4972,4994],{"className":4971},[581],[578,4973,4975],{"className":4974},[585],[587,4976,4977],{"xmlns":589},[591,4978,4979,4991],{},[594,4980,4981,4987,4989],{},[602,4982,4983,4985],{},[597,4984,956],{},[597,4986,609],{},[613,4988,4265],{},[947,4990,949],{},[624,4992,4993],{"encoding":626},"c_n \\geq 0",[578,4995,4997,5052],{"className":4996,"ariaHidden":632},[631],[578,4998,5000,5003,5043,5046,5049],{"className":4999},[636],[578,5001],{"className":5002,"style":998},[640],[578,5004,5006,5009],{"className":5005},[645],[578,5007,956],{"className":5008},[645,652],[578,5010,5012],{"className":5011},[656],[578,5013,5015,5035],{"className":5014},[660,661],[578,5016,5018,5032],{"className":5017},[665],[578,5019,5021],{"className":5020,"style":670},[669],[578,5022,5023,5026],{"style":673},[578,5024],{"className":5025,"style":678},[677],[578,5027,5029],{"className":5028},[682,683,684,685],[578,5030,609],{"className":5031},[645,652,685],[578,5033,693],{"className":5034},[692],[578,5036,5038],{"className":5037},[665],[578,5039,5041],{"className":5040,"style":700},[669],[578,5042],{},[578,5044],{"className":5045,"style":710},[709],[578,5047,4265],{"className":5048},[714],[578,5050],{"className":5051,"style":710},[709],[578,5053,5055,5058],{"className":5054},[636],[578,5056],{"className":5057,"style":1389},[640],[578,5059,949],{"className":5060},[645],[571,5062,5063,5064,5324],{},"Die Ungleichung in die falsche Richtung rechnen. Ein größerer Nenner macht den Bruch kleiner: ",[578,5065,5067,5106],{"className":5066},[581],[578,5068,5070],{"className":5069},[585],[587,5071,5072],{"xmlns":589},[591,5073,5074,5104],{},[594,5075,5076,5092,5094],{},[1409,5077,5078,5080],{},[947,5079,1352],{},[594,5081,5082,5088,5090],{},[1271,5083,5084,5086],{},[597,5085,609],{},[947,5087,2095],{},[613,5089,2098],{},[597,5091,609],{},[613,5093,615],{},[1409,5095,5096,5098],{},[947,5097,1352],{},[1271,5099,5100,5102],{},[597,5101,609],{},[947,5103,2095],{},[624,5105,2330],{"encoding":626},[578,5107,5109,5224],{"className":5108,"ariaHidden":632},[631],[578,5110,5112,5115,5215,5218,5221],{"className":5111},[636],[578,5113],{"className":5114,"style":2113},[640],[578,5116,5118,5121,5212],{"className":5117},[645],[578,5119],{"className":5120},[1444,1445],[578,5122,5124],{"className":5123},[1409],[578,5125,5127,5204],{"className":5126},[660,661],[578,5128,5130,5201],{"className":5129},[665],[578,5131,5133,5179,5187],{"className":5132,"style":1458},[669],[578,5134,5135,5138],{"style":1461},[578,5136],{"className":5137,"style":1465},[677],[578,5139,5141],{"className":5140},[682,683,684,685],[578,5142,5144,5173,5176],{"className":5143},[645,685],[578,5145,5147,5150],{"className":5146},[645,685],[578,5148,609],{"className":5149},[645,652,685],[578,5151,5153],{"className":5152},[656],[578,5154,5156],{"className":5155},[660],[578,5157,5159],{"className":5158},[665],[578,5160,5162],{"className":5161,"style":2231},[669],[578,5163,5164,5167],{"style":1493},[578,5165],{"className":5166,"style":1497},[677],[578,5168,5170],{"className":5169},[682,1501,1502,685],[578,5171,2095],{"className":5172},[645,685],[578,5174,2098],{"className":5175},[2246,685],[578,5177,609],{"className":5178},[645,652,685],[578,5180,5181,5184],{"style":1508},[578,5182],{"className":5183,"style":1465},[677],[578,5185],{"className":5186,"style":1516},[1515],[578,5188,5189,5192],{"style":1519},[578,5190],{"className":5191,"style":1465},[677],[578,5193,5195],{"className":5194},[682,683,684,685],[578,5196,5198],{"className":5197},[645,685],[578,5199,1352],{"className":5200},[645,685],[578,5202,693],{"className":5203},[692],[578,5205,5207],{"className":5206},[665],[578,5208,5210],{"className":5209,"style":2281},[669],[578,5211],{},[578,5213],{"className":5214},[1547,1445],[578,5216],{"className":5217,"style":710},[709],[578,5219,615],{"className":5220},[714],[578,5222],{"className":5223,"style":710},[709],[578,5225,5227,5230],{"className":5226},[636],[578,5228],{"className":5229,"style":1431},[640],[578,5231,5233,5236,5321],{"className":5232},[645],[578,5234],{"className":5235},[1444,1445],[578,5237,5239],{"className":5238},[1409],[578,5240,5242,5313],{"className":5241},[660,661],[578,5243,5245,5310],{"className":5244},[665],[578,5246,5248,5288,5296],{"className":5247,"style":1458},[669],[578,5249,5250,5253],{"style":1461},[578,5251],{"className":5252,"style":1465},[677],[578,5254,5256],{"className":5255},[682,683,684,685],[578,5257,5259],{"className":5258},[645,685],[578,5260,5262,5265],{"className":5261},[645,685],[578,5263,609],{"className":5264},[645,652,685],[578,5266,5268],{"className":5267},[656],[578,5269,5271],{"className":5270},[660],[578,5272,5274],{"className":5273},[665],[578,5275,5277],{"className":5276,"style":2231},[669],[578,5278,5279,5282],{"style":1493},[578,5280],{"className":5281,"style":1497},[677],[578,5283,5285],{"className":5284},[682,1501,1502,685],[578,5286,2095],{"className":5287},[645,685],[578,5289,5290,5293],{"style":1508},[578,5291],{"className":5292,"style":1465},[677],[578,5294],{"className":5295,"style":1516},[1515],[578,5297,5298,5301],{"style":1519},[578,5299],{"className":5300,"style":1465},[677],[578,5302,5304],{"className":5303},[682,683,684,685],[578,5305,5307],{"className":5306},[645,685],[578,5308,1352],{"className":5309},[645,685],[578,5311,693],{"className":5312},[692],[578,5314,5316],{"className":5315},[665],[578,5317,5319],{"className":5318,"style":1541},[669],[578,5320],{},[578,5322],{"className":5323},[1547,1445],", nicht umgekehrt.",{"title":5326,"searchDepth":5327,"depth":5327,"links":5328},"",2,[5329,5330,5331],{"id":561,"depth":5327,"text":562},{"id":2051,"depth":5327,"text":2052},{"id":4595,"depth":5327,"text":4596},[5333,5336,5339,5342,5345,5348],{"lhs":5334,"rhs":5335},"1\u002F(n^2 + n)","1\u002Fn - 1\u002F(n + 1)",{"lhs":5337,"rhs":5338},"sum(1 .\u002F ((1:99) .* (2:100)))","0.99",{"lhs":5340,"rhs":5341},"round(sum(1 .\u002F (2.^(1:60) + (1:60))), 4)","0.6973",{"lhs":5343,"rhs":5344},"sum(0.5.^(1:60))","1 - 0.5^60",{"lhs":5346,"rhs":5347},"round(sum(map(1:100, f(n) = 1\u002Fsqrt(n))), 2)","18.59",{"lhs":5349,"rhs":5350},"round(sum(1 .\u002F (1:100)), 2)","5.19","\\text{Ungleichung für alle } n \\geq N \\text{ (ab einem festen Index)}","\u003Cspan class=\"katex\">Ungleichung für alle\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmi>N\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\geq 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:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">N\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">(ab einem festen Index)\u003C\u002Fspan>",null,"md","comparison-test","|a_n| \\leq b_n \\text{ und } \\sum b_n \\text{ konvergent} \\;\\Rightarrow\\; \\sum a_n \\text{ absolut konvergent}","\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 mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmo>≤\u003C\u002Fmo>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmtext> und \u003C\u002Fmtext>\u003Cmo>∑\u003C\u002Fmo>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmtext> konvergent\u003C\u002Fmtext>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⇒\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>∑\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmtext> absolut konvergent\u003C\u002Fmtext>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">|a_n| \\leq b_n \\text{ und } \\sum b_n \\text{ konvergent} \\;\\Rightarrow\\; \\sum a_n \\text{ absolut konvergent}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\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:1.6em;vertical-align:-0.55em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\"> und \u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-symbol large-op\" style=\"position:relative;top:0em;\">∑\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\"> konvergent\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:1.6em;vertical-align:-0.55em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-symbol large-op\" style=\"position:relative;top:0em;\">∑\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\"> absolut konvergent\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fmajorantenkriterium",[],[5364,5365,5366,5367],"p-series","geometric-series","harmonic-series","integral-test",{"title":548,"description":5326},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fmajorantenkriterium","Lässt sich eine Reihe gliedweise durch eine konvergente Reihe abschätzen, konvergiert sie; liegt eine divergente darunter, divergiert sie.",[5372,5373,5374,5375,5376],"konvergenzkriterium","majorante","minorante","reihe","vergleichskriterium",[5378,5382,5386],{"symbol":5379,"meaning":5380,"symbolHtml":5381},"a_n","Glieder der untersuchten 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 encoding=\"application\u002Fx-tex\">a_n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":5383,"meaning":5384,"symbolHtml":5385},"b_n","Glieder der Vergleichsreihe (Majorante)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b_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:0.8444em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":5387,"meaning":5388,"symbolHtml":5389},"N","Index, ab dem die Abschätzung gilt","\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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">N\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","5GFDHNT8YWAyMhdS8omj8s6uWJHhvdhG6-NlMa_MGAI",[5392,5395,5398,5401],{"stem":5393,"title":5394,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fharmonische-reihe","Harmonische Reihe",{"stem":5396,"title":5397,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fintegralkriterium","Integralkriterium",{"stem":5399,"title":5400,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Funendliche-geometrische-reihe","Unendliche geometrische Reihe",{"stem":5402,"title":5403,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fverallgemeinerte-harmonische-reihe","Konvergenz der Reihe 1\u002Fnᵖ",1793824264413]