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Es gilt ",[568,1067,1069,1094],{"className":1068},[571],[568,1070,1072],{"className":1071},[575],[577,1073,1074],{"xmlns":579},[581,1075,1076,1091],{},[584,1077,1078,1086,1089],{},[1079,1080,1081,1083],"msub",{},[587,1082,589],{},[587,1084,1085],{},"n",[635,1087,1088],{},"→",[587,1090,589],{},[591,1092,1093],{"encoding":593},"a_n \\to 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genau dann, wenn ",[568,1180,1182,1204],{"className":1181},[571],[568,1183,1185],{"className":1184},[575],[577,1186,1187],{"xmlns":579},[581,1188,1189,1201],{},[584,1190,1191,1197,1199],{},[1079,1192,1193,1195],{},[587,1194,589],{},[587,1196,1085],{},[635,1198,701],{},[587,1200,589],{},[591,1202,1203],{"encoding":593},"a_n - a",[568,1205,1207,1263],{"className":1206,"ariaHidden":598},[597],[568,1208,1210,1214,1254,1257,1260],{"className":1209},[602],[568,1211],{"className":1212,"style":1213},[606],"height:0.7333em;vertical-align:-0.15em;",[568,1215,1217,1220],{"className":1216},[611],[568,1218,589],{"className":1219},[611,612],[568,1221,1223],{"className":1222},[1113],[568,1224,1226,1246],{"className":1225},[1117,1118],[568,1227,1229,1243],{"className":1228},[1122],[568,1230,1232],{"className":1231,"style":1127},[1126],[568,1233,1234,1237],{"style":1130},[568,1235],{"className":1236,"style":1135},[1134],[568,1238,1240],{"className":1239},[1139,1140,1141,1142],[568,1241,1085],{"className":1242},[611,612,1142],[568,1244,1150],{"className":1245},[1149],[568,1247,1249],{"className":1248},[1122],[568,1250,1252],{"className":1251,"style":1157},[1126],[568,1253],{},[568,1255],{"className":1256,"style":744},[661],[568,1258,701],{"className":1259},[748],[568,1261],{"className":1262,"style":744},[661],[568,1264,1266,1269],{"className":1265},[602],[568,1267],{"className":1268,"style":607},[606],[568,1270,589],{"className":1271},[611,612]," eine Nullfolge ist.",[564,1274,1275,1276,1380,1381,1506,1507,1535,1536,1564],{},"Im Beweis läuft es fast immer gleich: ",[568,1277,1279,1307],{"className":1278},[571],[568,1280,1282],{"className":1281},[575],[577,1283,1284],{"xmlns":579},[581,1285,1286,1304],{},[584,1287,1288,1292,1298,1300,1302],{},[587,1289,1291],{"mathvariant":1290},"normal","∣",[1079,1293,1294,1296],{},[587,1295,589],{},[587,1297,1085],{},[635,1299,701],{},[587,1301,589],{},[587,1303,1291],{"mathvariant":1290},[591,1305,1306],{"encoding":593},"|a_n - a|",[568,1308,1310,1368],{"className":1309,"ariaHidden":598},[597],[568,1311,1313,1316,1319,1359,1362,1365],{"className":1312},[602],[568,1314],{"className":1315,"style":733},[606],[568,1317,1291],{"className":1318},[611],[568,1320,1322,1325],{"className":1321},[611],[568,1323,589],{"className":1324},[611,612],[568,1326,1328],{"className":1327},[1113],[568,1329,1331,1351],{"className":1330},[1117,1118],[568,1332,1334,1348],{"className":1333},[1122],[568,1335,1337],{"className":1336,"style":1127},[1126],[568,1338,1339,1342],{"style":1130},[568,1340],{"className":1341,"style":1135},[1134],[568,1343,1345],{"className":1344},[1139,1140,1141,1142],[568,1346,1085],{"className":1347},[611,612,1142],[568,1349,1150],{"className":1350},[1149],[568,1352,1354],{"className":1353},[1122],[568,1355,1357],{"className":1356,"style":1157},[1126],[568,1358],{},[568,1360],{"className":1361,"style":744},[661],[568,1363,701],{"className":1364},[748],[568,1366],{"className":1367,"style":744},[661],[568,1369,1371,1374,1377],{"className":1370},[602],[568,1372],{"className":1373,"style":733},[606],[568,1375,589],{"className":1376},[611,612],[568,1378,1291],{"className":1379},[611]," vereinfachen oder nach oben abschätzen, die Ungleichung ",[568,1382,1384,1415],{"className":1383},[571],[568,1385,1387],{"className":1386},[575],[577,1388,1389],{"xmlns":579},[581,1390,1391,1412],{},[584,1392,1393,1395,1401,1403,1405,1407,1410],{},[587,1394,1291],{"mathvariant":1290},[1079,1396,1397,1399],{},[587,1398,589],{},[587,1400,1085],{},[635,1402,701],{},[587,1404,589],{},[587,1406,1291],{"mathvariant":1290},[635,1408,1409],{},"\u003C",[587,1411,633],{},[591,1413,1414],{"encoding":593},"|a_n - a| \u003C \\varepsilon",[568,1416,1418,1476,1497],{"className":1417,"ariaHidden":598},[597],[568,1419,1421,1424,1427,1467,1470,1473],{"className":1420},[602],[568,1422],{"className":1423,"style":733},[606],[568,1425,1291],{"className":1426},[611],[568,1428,1430,1433],{"className":1429},[611],[568,1431,589],{"className":1432},[611,612],[568,1434,1436],{"className":1435},[1113],[568,1437,1439,1459],{"className":1438},[1117,1118],[568,1440,1442,1456],{"className":1441},[1122],[568,1443,1445],{"className":1444,"style":1127},[1126],[568,1446,1447,1450],{"style":1130},[568,1448],{"className":1449,"style":1135},[1134],[568,1451,1453],{"className":1452},[1139,1140,1141,1142],[568,1454,1085],{"className":1455},[611,612,1142],[568,1457,1150],{"className":1458},[1149],[568,1460,1462],{"className":1461},[1122],[568,1463,1465],{"className":1464,"style":1157},[1126],[568,1466],{},[568,1468],{"className":1469,"style":744},[661],[568,1471,701],{"className":1472},[748],[568,1474],{"className":1475,"style":744},[661],[568,1477,1479,1482,1485,1488,1491,1494],{"className":1478},[602],[568,1480],{"className":1481,"style":733},[606],[568,1483,589],{"className":1484},[611,612],[568,1486,1291],{"className":1487},[611],[568,1489],{"className":1490,"style":662},[661],[568,1492,1409],{"className":1493},[666],[568,1495],{"className":1496,"style":662},[661],[568,1498,1500,1503],{"className":1499},[602],[568,1501],{"className":1502,"style":607},[606],[568,1504,633],{"className":1505},[611,612]," nach ",[568,1508,1510,1523],{"className":1509},[571],[568,1511,1513],{"className":1512},[575],[577,1514,1515],{"xmlns":579},[581,1516,1517,1521],{},[584,1518,1519],{},[587,1520,1085],{},[591,1522,1085],{"encoding":593},[568,1524,1526],{"className":1525,"ariaHidden":598},[597],[568,1527,1529,1532],{"className":1528},[602],[568,1530],{"className":1531,"style":607},[606],[568,1533,1085],{"className":1534},[611,612]," auflösen und daraus ein passendes ",[568,1537,1539,1552],{"className":1538},[571],[568,1540,1542],{"className":1541},[575],[577,1543,1544],{"xmlns":579},[581,1545,1546,1550],{},[584,1547,1548],{},[587,1549,879],{},[591,1551,879],{"encoding":593},[568,1553,1555],{"className":1554,"ariaHidden":598},[597],[568,1556,1558,1561],{"className":1557},[602],[568,1559],{"className":1560,"style":891},[606],[568,1562,879],{"className":1563,"style":895},[611,612]," ablesen.",[559,1566,1568],{"id":1567},"beispiele","Beispiele",[564,1570,1571,1745,1746,1981,1982,2102,2103,2166,2167,2219,2220,2383,2384,2514],{},[568,1572,1574,1603],{"className":1573},[571],[568,1575,1577],{"className":1576},[575],[577,1578,1579],{"xmlns":579},[581,1580,1581,1600],{},[584,1582,1583,1589,1592],{},[1079,1584,1585,1587],{},[587,1586,589],{},[587,1588,1085],{},[635,1590,1591],{},"=",[1593,1594,1595,1598],"mfrac",{},[639,1596,1597],{},"1",[587,1599,1085],{},[591,1601,1602],{"encoding":593},"a_n = \\frac{1}{n}",[568,1604,1606,1661],{"className":1605,"ariaHidden":598},[597],[568,1607,1609,1612,1652,1655,1658],{"className":1608},[602],[568,1610],{"className":1611,"style":1103},[606],[568,1613,1615,1618],{"className":1614},[611],[568,1616,589],{"className":1617},[611,612],[568,1619,1621],{"className":1620},[1113],[568,1622,1624,1644],{"className":1623},[1117,1118],[568,1625,1627,1641],{"className":1626},[1122],[568,1628,1630],{"className":1629,"style":1127},[1126],[568,1631,1632,1635],{"style":1130},[568,1633],{"className":1634,"style":1135},[1134],[568,1636,1638],{"className":1637},[1139,1140,1141,1142],[568,1639,1085],{"className":1640},[611,612,1142],[568,1642,1150],{"className":1643},[1149],[568,1645,1647],{"className":1646},[1122],[568,1648,1650],{"className":1649,"style":1157},[1126],[568,1651],{},[568,1653],{"className":1654,"style":662},[661],[568,1656,1591],{"className":1657},[666],[568,1659],{"className":1660,"style":662},[661],[568,1662,1664,1668],{"className":1663},[602],[568,1665],{"className":1666,"style":1667},[606],"height:1.1901em;vertical-align:-0.345em;",[568,1669,1671,1675,1742],{"className":1670},[611],[568,1672],{"className":1673},[737,1674],"nulldelimiter",[568,1676,1678],{"className":1677},[1593],[568,1679,1681,1733],{"className":1680},[1117,1118],[568,1682,1684,1730],{"className":1683},[1122],[568,1685,1688,1704,1715],{"className":1686,"style":1687},[1126],"height:0.8451em;",[568,1689,1691,1695],{"style":1690},"top:-2.655em;",[568,1692],{"className":1693,"style":1694},[1134],"height:3em;",[568,1696,1698],{"className":1697},[1139,1140,1141,1142],[568,1699,1701],{"className":1700},[611,1142],[568,1702,1085],{"className":1703},[611,612,1142],[568,1705,1707,1710],{"style":1706},"top:-3.23em;",[568,1708],{"className":1709,"style":1694},[1134],[568,1711],{"className":1712,"style":1714},[1713],"frac-line","border-bottom-width:0.04em;",[568,1716,1718,1721],{"style":1717},"top:-3.394em;",[568,1719],{"className":1720,"style":1694},[1134],[568,1722,1724],{"className":1723},[1139,1140,1141,1142],[568,1725,1727],{"className":1726},[611,1142],[568,1728,1597],{"className":1729},[611,1142],[568,1731,1150],{"className":1732},[1149],[568,1734,1736],{"className":1735},[1122],[568,1737,1740],{"className":1738,"style":1739},[1126],"height:0.345em;",[568,1741],{},[568,1743],{"className":1744},[797,1674]," ist eine Nullfolge: ",[568,1747,1749,1781],{"className":1748},[571],[568,1750,1752],{"className":1751},[575],[577,1753,1754],{"xmlns":579},[581,1755,1756,1778],{},[584,1757,1758,1774,1776],{},[584,1759,1760,1762,1768,1770,1772],{},[635,1761,1291],{"fence":598},[1593,1763,1764,1766],{},[639,1765,1597],{},[587,1767,1085],{},[635,1769,701],{},[639,1771,641],{},[635,1773,1291],{"fence":598},[635,1775,1409],{},[587,1777,633],{},[591,1779,1780],{"encoding":593},"\\left|\\frac{1}{n} - 0\\right| \u003C \\varepsilon",[568,1782,1784,1972],{"className":1783,"ariaHidden":598},[597],[568,1785,1787,1791,1963,1966,1969],{"className":1786},[602],[568,1788],{"className":1789,"style":1790},[606],"height:1.2em;vertical-align:-0.35em;",[568,1792,1795,1846,1914,1917,1920,1923,1926],{"className":1793},[1794],"minner",[568,1796,1798],{"className":1797},[737],[568,1799,1803],{"className":1800},[1801,1802],"delimsizing","mult",[568,1804,1806,1837],{"className":1805},[1117,1118],[568,1807,1809,1834],{"className":1808},[1122],[568,1810,1813],{"className":1811,"style":1812},[1126],"height:0.85em;",[568,1814,1816,1820],{"style":1815},"top:-2.85em;",[568,1817],{"className":1818,"style":1819},[1134],"height:3.2em;",[568,1821,1823],{"style":1822},"width:0.333em;height:1.2em;",[1824,1825,1830],"svg",{"xmlns":1826,"width":1827,"height":1828,"viewBox":1829},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","0.333em","1.2em","0 0 333 1200",[1831,1832],"path",{"d":1833},"M145 15 v585 v0 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v0 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v0 v585 h43z",[568,1835,1150],{"className":1836},[1149],[568,1838,1840],{"className":1839},[1122],[568,1841,1844],{"className":1842,"style":1843},[1126],"height:0.35em;",[568,1845],{},[568,1847,1849,1852,1911],{"className":1848},[611],[568,1850],{"className":1851},[737,1674],[568,1853,1855],{"className":1854},[1593],[568,1856,1858,1903],{"className":1857},[1117,1118],[568,1859,1861,1900],{"className":1860},[1122],[568,1862,1864,1878,1886],{"className":1863,"style":1687},[1126],[568,1865,1866,1869],{"style":1690},[568,1867],{"className":1868,"style":1694},[1134],[568,1870,1872],{"className":1871},[1139,1140,1141,1142],[568,1873,1875],{"className":1874},[611,1142],[568,1876,1085],{"className":1877},[611,612,1142],[568,1879,1880,1883],{"style":1706},[568,1881],{"className":1882,"style":1694},[1134],[568,1884],{"className":1885,"style":1714},[1713],[568,1887,1888,1891],{"style":1717},[568,1889],{"className":1890,"style":1694},[1134],[568,1892,1894],{"className":1893},[1139,1140,1141,1142],[568,1895,1897],{"className":1896},[611,1142],[568,1898,1597],{"className":1899},[611,1142],[568,1901,1150],{"className":1902},[1149],[568,1904,1906],{"className":1905},[1122],[568,1907,1909],{"className":1908,"style":1739},[1126],[568,1910],{},[568,1912],{"className":1913},[797,1674],[568,1915],{"className":1916,"style":744},[661],[568,1918,701],{"className":1919},[748],[568,1921],{"className":1922,"style":744},[661],[568,1924,641],{"className":1925},[611],[568,1927,1929],{"className":1928},[797],[568,1930,1932],{"className":1931},[1801,1802],[568,1933,1935,1955],{"className":1934},[1117,1118],[568,1936,1938,1952],{"className":1937},[1122],[568,1939,1941],{"className":1940,"style":1812},[1126],[568,1942,1943,1946],{"style":1815},[568,1944],{"className":1945,"style":1819},[1134],[568,1947,1948],{"style":1822},[1824,1949,1950],{"xmlns":1826,"width":1827,"height":1828,"viewBox":1829},[1831,1951],{"d":1833},[568,1953,1150],{"className":1954},[1149],[568,1956,1958],{"className":1957},[1122],[568,1959,1961],{"className":1960,"style":1843},[1126],[568,1962],{},[568,1964],{"className":1965,"style":662},[661],[568,1967,1409],{"className":1968},[666],[568,1970],{"className":1971,"style":662},[661],[568,1973,1975,1978],{"className":1974},[602],[568,1976],{"className":1977,"style":607},[606],[568,1979,633],{"className":1980},[611,612]," gilt für ",[568,1983,1985,2007],{"className":1984},[571],[568,1986,1988],{"className":1987},[575],[577,1989,1990],{"xmlns":579},[581,1991,1992,2004],{},[584,1993,1994,1996,1998],{},[587,1995,1085],{},[635,1997,637],{},[1593,1999,2000,2002],{},[639,2001,1597],{},[587,2003,633],{},[591,2005,2006],{"encoding":593},"n > \\frac{1}{\\varepsilon}",[568,2008,2010,2028],{"className":2009,"ariaHidden":598},[597],[568,2011,2013,2016,2019,2022,2025],{"className":2012},[602],[568,2014],{"className":2015,"style":654},[606],[568,2017,1085],{"className":2018},[611,612],[568,2020],{"className":2021,"style":662},[661],[568,2023,637],{"className":2024},[666],[568,2026],{"className":2027,"style":662},[661],[568,2029,2031,2034],{"className":2030},[602],[568,2032],{"className":2033,"style":1667},[606],[568,2035,2037,2040,2099],{"className":2036},[611],[568,2038],{"className":2039},[737,1674],[568,2041,2043],{"className":2042},[1593],[568,2044,2046,2091],{"className":2045},[1117,1118],[568,2047,2049,2088],{"className":2048},[1122],[568,2050,2052,2066,2074],{"className":2051,"style":1687},[1126],[568,2053,2054,2057],{"style":1690},[568,2055],{"className":2056,"style":1694},[1134],[568,2058,2060],{"className":2059},[1139,1140,1141,1142],[568,2061,2063],{"className":2062},[611,1142],[568,2064,633],{"className":2065},[611,612,1142],[568,2067,2068,2071],{"style":1706},[568,2069],{"className":2070,"style":1694},[1134],[568,2072],{"className":2073,"style":1714},[1713],[568,2075,2076,2079],{"style":1717},[568,2077],{"className":2078,"style":1694},[1134],[568,2080,2082],{"className":2081},[1139,1140,1141,1142],[568,2083,2085],{"className":2084},[611,1142],[568,2086,1597],{"className":2087},[611,1142],[568,2089,1150],{"className":2090},[1149],[568,2092,2094],{"className":2093},[1122],[568,2095,2097],{"className":2096,"style":1739},[1126],[568,2098],{},[568,2100],{"className":2101},[797,1674],". Zu ",[568,2104,2106,2125],{"className":2105},[571],[568,2107,2109],{"className":2108},[575],[577,2110,2111],{"xmlns":579},[581,2112,2113,2122],{},[584,2114,2115,2117,2119],{},[587,2116,633],{},[635,2118,1591],{},[639,2120,2121],{},"0,01",[591,2123,2124],{"encoding":593},"\\varepsilon = 0{,}01",[568,2126,2128,2146],{"className":2127,"ariaHidden":598},[597],[568,2129,2131,2134,2137,2140,2143],{"className":2130},[602],[568,2132],{"className":2133,"style":607},[606],[568,2135,633],{"className":2136},[611,612],[568,2138],{"className":2139,"style":662},[661],[568,2141,1591],{"className":2142},[666],[568,2144],{"className":2145,"style":662},[661],[568,2147,2149,2153,2156,2162],{"className":2148},[602],[568,2150],{"className":2151,"style":2152},[606],"height:0.8389em;vertical-align:-0.1944em;",[568,2154,641],{"className":2155},[611],[568,2157,2159],{"className":2158},[611],[568,2160,706],{"className":2161},[765],[568,2163,2165],{"className":2164},[611],"01"," passt also ",[568,2168,2170,2189],{"className":2169},[571],[568,2171,2173],{"className":2172},[575],[577,2174,2175],{"xmlns":579},[581,2176,2177,2186],{},[584,2178,2179,2181,2183],{},[587,2180,879],{},[635,2182,1591],{},[639,2184,2185],{},"101",[591,2187,2188],{"encoding":593},"N = 101",[568,2190,2192,2210],{"className":2191,"ariaHidden":598},[597],[568,2193,2195,2198,2201,2204,2207],{"className":2194},[602],[568,2196],{"className":2197,"style":891},[606],[568,2199,879],{"className":2200,"style":895},[611,612],[568,2202],{"className":2203,"style":662},[661],[568,2205,1591],{"className":2206},[666],[568,2208],{"className":2209,"style":662},[661],[568,2211,2213,2216],{"className":2212},[602],[568,2214],{"className":2215,"style":676},[606],[568,2217,2185],{"className":2218},[611],", denn ",[568,2221,2223,2251],{"className":2222},[571],[568,2224,2226],{"className":2225},[575],[577,2227,2228],{"xmlns":579},[581,2229,2230,2248],{},[584,2231,2232,2238,2241,2244,2246],{},[1593,2233,2234,2236],{},[639,2235,1597],{},[639,2237,2185],{},[635,2239,2240],{},"≈",[639,2242,2243],{},"0,009901",[635,2245,1409],{},[639,2247,2121],{},[591,2249,2250],{"encoding":593},"\\frac{1}{101} \\approx 0{,}009901 \u003C 0{,}01",[568,2252,2254,2337,2365],{"className":2253,"ariaHidden":598},[597],[568,2255,2257,2260,2328,2331,2334],{"className":2256},[602],[568,2258],{"className":2259,"style":1667},[606],[568,2261,2263,2266,2325],{"className":2262},[611],[568,2264],{"className":2265},[737,1674],[568,2267,2269],{"className":2268},[1593],[568,2270,2272,2317],{"className":2271},[1117,1118],[568,2273,2275,2314],{"className":2274},[1122],[568,2276,2278,2292,2300],{"className":2277,"style":1687},[1126],[568,2279,2280,2283],{"style":1690},[568,2281],{"className":2282,"style":1694},[1134],[568,2284,2286],{"className":2285},[1139,1140,1141,1142],[568,2287,2289],{"className":2288},[611,1142],[568,2290,2185],{"className":2291},[611,1142],[568,2293,2294,2297],{"style":1706},[568,2295],{"className":2296,"style":1694},[1134],[568,2298],{"className":2299,"style":1714},[1713],[568,2301,2302,2305],{"style":1717},[568,2303],{"className":2304,"style":1694},[1134],[568,2306,2308],{"className":2307},[1139,1140,1141,1142],[568,2309,2311],{"className":2310},[611,1142],[568,2312,1597],{"className":2313},[611,1142],[568,2315,1150],{"className":2316},[1149],[568,2318,2320],{"className":2319},[1122],[568,2321,2323],{"className":2322,"style":1739},[1126],[568,2324],{},[568,2326],{"className":2327},[797,1674],[568,2329],{"className":2330,"style":662},[661],[568,2332,2240],{"className":2333},[666],[568,2335],{"className":2336,"style":662},[661],[568,2338,2340,2343,2346,2352,2356,2359,2362],{"className":2339},[602],[568,2341],{"className":2342,"style":2152},[606],[568,2344,641],{"className":2345},[611],[568,2347,2349],{"className":2348},[611],[568,2350,706],{"className":2351},[765],[568,2353,2355],{"className":2354},[611],"009901",[568,2357],{"className":2358,"style":662},[661],[568,2360,1409],{"className":2361},[666],[568,2363],{"className":2364,"style":662},[661],[568,2366,2368,2371,2374,2380],{"className":2367},[602],[568,2369],{"className":2370,"style":2152},[606],[568,2372,641],{"className":2373},[611],[568,2375,2377],{"className":2376},[611],[568,2378,706],{"className":2379},[765],[568,2381,2165],{"className":2382},[611],", während ",[568,2385,2387,2410],{"className":2386},[571],[568,2388,2390],{"className":2389},[575],[577,2391,2392],{"xmlns":579},[581,2393,2394,2407],{},[584,2395,2396,2403,2405],{},[1593,2397,2398,2400],{},[639,2399,1597],{},[639,2401,2402],{},"100",[635,2404,1591],{},[639,2406,2121],{},[591,2408,2409],{"encoding":593},"\\frac{1}{100} = 0{,}01",[568,2411,2413,2496],{"className":2412,"ariaHidden":598},[597],[568,2414,2416,2419,2487,2490,2493],{"className":2415},[602],[568,2417],{"className":2418,"style":1667},[606],[568,2420,2422,2425,2484],{"className":2421},[611],[568,2423],{"className":2424},[737,1674],[568,2426,2428],{"className":2427},[1593],[568,2429,2431,2476],{"className":2430},[1117,1118],[568,2432,2434,2473],{"className":2433},[1122],[568,2435,2437,2451,2459],{"className":2436,"style":1687},[1126],[568,2438,2439,2442],{"style":1690},[568,2440],{"className":2441,"style":1694},[1134],[568,2443,2445],{"className":2444},[1139,1140,1141,1142],[568,2446,2448],{"className":2447},[611,1142],[568,2449,2402],{"className":2450},[611,1142],[568,2452,2453,2456],{"style":1706},[568,2454],{"className":2455,"style":1694},[1134],[568,2457],{"className":2458,"style":1714},[1713],[568,2460,2461,2464],{"style":1717},[568,2462],{"className":2463,"style":1694},[1134],[568,2465,2467],{"className":2466},[1139,1140,1141,1142],[568,2468,2470],{"className":2469},[611,1142],[568,2471,1597],{"className":2472},[611,1142],[568,2474,1150],{"className":2475},[1149],[568,2477,2479],{"className":2478},[1122],[568,2480,2482],{"className":2481,"style":1739},[1126],[568,2483],{},[568,2485],{"className":2486},[797,1674],[568,2488],{"className":2489,"style":662},[661],[568,2491,1591],{"className":2492},[666],[568,2494],{"className":2495,"style":662},[661],[568,2497,2499,2502,2505,2511],{"className":2498},[602],[568,2500],{"className":2501,"style":2152},[606],[568,2503,641],{"className":2504},[611],[568,2506,2508],{"className":2507},[611],[568,2509,706],{"className":2510},[765],[568,2512,2165],{"className":2513},[611]," gerade nicht mehr kleiner ist.",[564,2516,2517,2710,2711,2739],{},[568,2518,2520,2561],{"className":2519},[571],[568,2521,2523],{"className":2522},[575],[577,2524,2525],{"xmlns":579},[581,2526,2527,2558],{},[584,2528,2529,2535,2537],{},[1079,2530,2531,2533],{},[587,2532,589],{},[587,2534,1085],{},[635,2536,1591],{},[1593,2538,2539,2550],{},[584,2540,2541,2544,2546,2548],{},[639,2542,2543],{},"2",[587,2545,1085],{},[635,2547,715],{},[639,2549,1597],{},[584,2551,2552,2554,2556],{},[587,2553,1085],{},[635,2555,715],{},[639,2557,1597],{},[591,2559,2560],{"encoding":593},"a_n = \\frac{2n + 1}{n + 1}",[568,2562,2564,2619],{"className":2563,"ariaHidden":598},[597],[568,2565,2567,2570,2610,2613,2616],{"className":2566},[602],[568,2568],{"className":2569,"style":1103},[606],[568,2571,2573,2576],{"className":2572},[611],[568,2574,589],{"className":2575},[611,612],[568,2577,2579],{"className":2578},[1113],[568,2580,2582,2602],{"className":2581},[1117,1118],[568,2583,2585,2599],{"className":2584},[1122],[568,2586,2588],{"className":2587,"style":1127},[1126],[568,2589,2590,2593],{"style":1130},[568,2591],{"className":2592,"style":1135},[1134],[568,2594,2596],{"className":2595},[1139,1140,1141,1142],[568,2597,1085],{"className":2598},[611,612,1142],[568,2600,1150],{"className":2601},[1149],[568,2603,2605],{"className":2604},[1122],[568,2606,2608],{"className":2607,"style":1157},[1126],[568,2609],{},[568,2611],{"className":2612,"style":662},[661],[568,2614,1591],{"className":2615},[666],[568,2617],{"className":2618,"style":662},[661],[568,2620,2622,2626],{"className":2621},[602],[568,2623],{"className":2624,"style":2625},[606],"height:1.2484em;vertical-align:-0.4033em;",[568,2627,2629,2632,2707],{"className":2628},[611],[568,2630],{"className":2631},[737,1674],[568,2633,2635],{"className":2634},[1593],[568,2636,2638,2698],{"className":2637},[1117,1118],[568,2639,2641,2695],{"className":2640},[1122],[568,2642,2644,2664,2672],{"className":2643,"style":1687},[1126],[568,2645,2646,2649],{"style":1690},[568,2647],{"className":2648,"style":1694},[1134],[568,2650,2652],{"className":2651},[1139,1140,1141,1142],[568,2653,2655,2658,2661],{"className":2654},[611,1142],[568,2656,1085],{"className":2657},[611,612,1142],[568,2659,715],{"className":2660},[748,1142],[568,2662,1597],{"className":2663},[611,1142],[568,2665,2666,2669],{"style":1706},[568,2667],{"className":2668,"style":1694},[1134],[568,2670],{"className":2671,"style":1714},[1713],[568,2673,2674,2677],{"style":1717},[568,2675],{"className":2676,"style":1694},[1134],[568,2678,2680],{"className":2679},[1139,1140,1141,1142],[568,2681,2683,2686,2689,2692],{"className":2682},[611,1142],[568,2684,2543],{"className":2685},[611,1142],[568,2687,1085],{"className":2688},[611,612,1142],[568,2690,715],{"className":2691},[748,1142],[568,2693,1597],{"className":2694},[611,1142],[568,2696,1150],{"className":2697},[1149],[568,2699,2701],{"className":2700},[1122],[568,2702,2705],{"className":2703,"style":2704},[1126],"height:0.4033em;",[568,2706],{},[568,2708],{"className":2709},[797,1674]," konvergiert gegen ",[568,2712,2714,2727],{"className":2713},[571],[568,2715,2717],{"className":2716},[575],[577,2718,2719],{"xmlns":579},[581,2720,2721,2725],{},[584,2722,2723],{},[639,2724,2543],{},[591,2726,2543],{"encoding":593},[568,2728,2730],{"className":2729,"ariaHidden":598},[597],[568,2731,2733,2736],{"className":2732},[602],[568,2734],{"className":2735,"style":676},[606],[568,2737,2543],{"className":2738},[611],":",[568,2741,2744],{"className":2742},[2743],"katex-display",[568,2745,2747,2856],{"className":2746},[571],[568,2748,2750],{"className":2749},[575],[577,2751,2753],{"xmlns":579,"display":2752},"block",[581,2754,2755,2853],{},[584,2756,2757,2759,2765,2767,2769,2771,2773,2813,2815,2827,2829,2831,2834,2837,2839,2841,2843,2849,2851],{},[587,2758,1291],{"mathvariant":1290},[1079,2760,2761,2763],{},[587,2762,589],{},[587,2764,1085],{},[635,2766,701],{},[639,2768,2543],{},[587,2770,1291],{"mathvariant":1290},[635,2772,1591],{},[584,2774,2775,2777,2811],{},[635,2776,1291],{"fence":598},[1593,2778,2779,2803],{},[584,2780,2781,2783,2785,2787,2789,2791,2793,2795,2797,2799,2801],{},[639,2782,2543],{},[587,2784,1085],{},[635,2786,715],{},[639,2788,1597],{},[635,2790,701],{},[639,2792,2543],{},[635,2794,696],{"stretchy":695},[587,2796,1085],{},[635,2798,715],{},[639,2800,1597],{},[635,2802,720],{"stretchy":695},[584,2804,2805,2807,2809],{},[587,2806,1085],{},[635,2808,715],{},[639,2810,1597],{},[635,2812,1291],{"fence":598},[635,2814,1591],{},[1593,2816,2817,2819],{},[639,2818,1597],{},[584,2820,2821,2823,2825],{},[587,2822,1085],{},[635,2824,715],{},[639,2826,1597],{},[635,2828,1409],{},[587,2830,633],{},[708,2832,2833],{},"  ",[635,2835,2836],{},"⇔",[708,2838,2833],{},[587,2840,1085],{},[635,2842,637],{},[1593,2844,2845,2847],{},[639,2846,1597],{},[587,2848,633],{},[635,2850,701],{},[639,2852,1597],{},[591,2854,2855],{"encoding":593},"|a_n - 2| = \\left| \\frac{2n + 1 - 2(n + 1)}{n + 1} \\right| = \\frac{1}{n + 1} \u003C \\varepsilon \\;\\Leftrightarrow\\; n > \\frac{1}{\\varepsilon} - 1",[568,2857,2859,2917,2936,3163,3254,3278,3296,3375],{"className":2858,"ariaHidden":598},[597],[568,2860,2862,2865,2868,2908,2911,2914],{"className":2861},[602],[568,2863],{"className":2864,"style":733},[606],[568,2866,1291],{"className":2867},[611],[568,2869,2871,2874],{"className":2870},[611],[568,2872,589],{"className":2873},[611,612],[568,2875,2877],{"className":2876},[1113],[568,2878,2880,2900],{"className":2879},[1117,1118],[568,2881,2883,2897],{"className":2882},[1122],[568,2884,2886],{"className":2885,"style":1127},[1126],[568,2887,2888,2891],{"style":1130},[568,2889],{"className":2890,"style":1135},[1134],[568,2892,2894],{"className":2893},[1139,1140,1141,1142],[568,2895,1085],{"className":2896},[611,612,1142],[568,2898,1150],{"className":2899},[1149],[568,2901,2903],{"className":2902},[1122],[568,2904,2906],{"className":2905,"style":1157},[1126],[568,2907],{},[568,2909],{"className":2910,"style":744},[661],[568,2912,701],{"className":2913},[748],[568,2915],{"className":2916,"style":744},[661],[568,2918,2920,2923,2927,2930,2933],{"className":2919},[602],[568,2921],{"className":2922,"style":733},[606],[568,2924,2926],{"className":2925},[611],"2∣",[568,2928],{"className":2929,"style":662},[661],[568,2931,1591],{"className":2932},[666],[568,2934],{"className":2935,"style":662},[661],[568,2937,2939,2943,3154,3157,3160],{"className":2938},[602],[568,2940],{"className":2941,"style":2942},[606],"height:2.4em;vertical-align:-0.95em;",[568,2944,2946,2991,3117],{"className":2945},[1794],[568,2947,2949],{"className":2948},[737],[568,2950,2952],{"className":2951},[1801,1802],[568,2953,2955,2982],{"className":2954},[1117,1118],[568,2956,2958,2979],{"className":2957},[1122],[568,2959,2962],{"className":2960,"style":2961},[1126],"height:1.45em;",[568,2963,2965,2969],{"style":2964},"top:-3.45em;",[568,2966],{"className":2967,"style":2968},[1134],"height:4.4em;",[568,2970,2972],{"style":2971},"width:0.333em;height:2.4em;",[1824,2973,2976],{"xmlns":1826,"width":1827,"height":2974,"viewBox":2975},"2.4em","0 0 333 2400",[1831,2977],{"d":2978},"M145 15 v585 v1200 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v-1200 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v1200 v585 h43z",[568,2980,1150],{"className":2981},[1149],[568,2983,2985],{"className":2984},[1122],[568,2986,2989],{"className":2987,"style":2988},[1126],"height:0.95em;",[568,2990],{},[568,2992,2994,2997,3114],{"className":2993},[611],[568,2995],{"className":2996},[737,1674],[568,2998,3000],{"className":2999},[1593],[568,3001,3003,3105],{"className":3002},[1117,1118],[568,3004,3006,3102],{"className":3005},[1122],[568,3007,3010,3034,3042],{"className":3008,"style":3009},[1126],"height:1.427em;",[568,3011,3013,3016],{"style":3012},"top:-2.314em;",[568,3014],{"className":3015,"style":1694},[1134],[568,3017,3019,3022,3025,3028,3031],{"className":3018},[611],[568,3020,1085],{"className":3021},[611,612],[568,3023],{"className":3024,"style":744},[661],[568,3026,715],{"className":3027},[748],[568,3029],{"className":3030,"style":744},[661],[568,3032,1597],{"className":3033},[611],[568,3035,3036,3039],{"style":1706},[568,3037],{"className":3038,"style":1694},[1134],[568,3040],{"className":3041,"style":1714},[1713],[568,3043,3045,3048],{"style":3044},"top:-3.677em;",[568,3046],{"className":3047,"style":1694},[1134],[568,3049,3051,3054,3057,3060,3063,3066,3069,3072,3075,3078,3081,3084,3087,3090,3093,3096,3099],{"className":3050},[611],[568,3052,2543],{"className":3053},[611],[568,3055,1085],{"className":3056},[611,612],[568,3058],{"className":3059,"style":744},[661],[568,3061,715],{"className":3062},[748],[568,3064],{"className":3065,"style":744},[661],[568,3067,1597],{"className":3068},[611],[568,3070],{"className":3071,"style":744},[661],[568,3073,701],{"className":3074},[748],[568,3076],{"className":3077,"style":744},[661],[568,3079,2543],{"className":3080},[611],[568,3082,696],{"className":3083},[737],[568,3085,1085],{"className":3086},[611,612],[568,3088],{"className":3089,"style":744},[661],[568,3091,715],{"className":3092},[748],[568,3094],{"className":3095,"style":744},[661],[568,3097,1597],{"className":3098},[611],[568,3100,720],{"className":3101},[797],[568,3103,1150],{"className":3104},[1149],[568,3106,3108],{"className":3107},[1122],[568,3109,3112],{"className":3110,"style":3111},[1126],"height:0.7693em;",[568,3113],{},[568,3115],{"className":3116},[797,1674],[568,3118,3120],{"className":3119},[797],[568,3121,3123],{"className":3122},[1801,1802],[568,3124,3126,3146],{"className":3125},[1117,1118],[568,3127,3129,3143],{"className":3128},[1122],[568,3130,3132],{"className":3131,"style":2961},[1126],[568,3133,3134,3137],{"style":2964},[568,3135],{"className":3136,"style":2968},[1134],[568,3138,3139],{"style":2971},[1824,3140,3141],{"xmlns":1826,"width":1827,"height":2974,"viewBox":2975},[1831,3142],{"d":2978},[568,3144,1150],{"className":3145},[1149],[568,3147,3149],{"className":3148},[1122],[568,3150,3152],{"className":3151,"style":2988},[1126],[568,3153],{},[568,3155],{"className":3156,"style":662},[661],[568,3158,1591],{"className":3159},[666],[568,3161],{"className":3162,"style":662},[661],[568,3164,3166,3170,3245,3248,3251],{"className":3165},[602],[568,3167],{"className":3168,"style":3169},[606],"height:2.0908em;vertical-align:-0.7693em;",[568,3171,3173,3176,3242],{"className":3172},[611],[568,3174],{"className":3175},[737,1674],[568,3177,3179],{"className":3178},[1593],[568,3180,3182,3234],{"className":3181},[1117,1118],[568,3183,3185,3231],{"className":3184},[1122],[568,3186,3189,3212,3220],{"className":3187,"style":3188},[1126],"height:1.3214em;",[568,3190,3191,3194],{"style":3012},[568,3192],{"className":3193,"style":1694},[1134],[568,3195,3197,3200,3203,3206,3209],{"className":3196},[611],[568,3198,1085],{"className":3199},[611,612],[568,3201],{"className":3202,"style":744},[661],[568,3204,715],{"className":3205},[748],[568,3207],{"className":3208,"style":744},[661],[568,3210,1597],{"className":3211},[611],[568,3213,3214,3217],{"style":1706},[568,3215],{"className":3216,"style":1694},[1134],[568,3218],{"className":3219,"style":1714},[1713],[568,3221,3222,3225],{"style":3044},[568,3223],{"className":3224,"style":1694},[1134],[568,3226,3228],{"className":3227},[611],[568,3229,1597],{"className":3230},[611],[568,3232,1150],{"className":3233},[1149],[568,3235,3237],{"className":3236},[1122],[568,3238,3240],{"className":3239,"style":3111},[1126],[568,3241],{},[568,3243],{"className":3244},[797,1674],[568,3246],{"className":3247,"style":662},[661],[568,3249,1409],{"className":3250},[666],[568,3252],{"className":3253,"style":662},[661],[568,3255,3257,3260,3263,3266,3269,3272,3275],{"className":3256},[602],[568,3258],{"className":3259,"style":607},[606],[568,3261,633],{"className":3262},[611,612],[568,3264],{"className":3265,"style":662},[661],[568,3267],{"className":3268,"style":662},[661],[568,3270,2836],{"className":3271},[666],[568,3273],{"className":3274,"style":662},[661],[568,3276],{"className":3277,"style":662},[661],[568,3279,3281,3284,3287,3290,3293],{"className":3280},[602],[568,3282],{"className":3283,"style":654},[606],[568,3285,1085],{"className":3286},[611,612],[568,3288],{"className":3289,"style":662},[661],[568,3291,637],{"className":3292},[666],[568,3294],{"className":3295,"style":662},[661],[568,3297,3299,3303,3366,3369,3372],{"className":3298},[602],[568,3300],{"className":3301,"style":3302},[606],"height:2.0074em;vertical-align:-0.686em;",[568,3304,3306,3309,3363],{"className":3305},[611],[568,3307],{"className":3308},[737,1674],[568,3310,3312],{"className":3311},[1593],[568,3313,3315,3354],{"className":3314},[1117,1118],[568,3316,3318,3351],{"className":3317},[1122],[568,3319,3321,3332,3340],{"className":3320,"style":3188},[1126],[568,3322,3323,3326],{"style":3012},[568,3324],{"className":3325,"style":1694},[1134],[568,3327,3329],{"className":3328},[611],[568,3330,633],{"className":3331},[611,612],[568,3333,3334,3337],{"style":1706},[568,3335],{"className":3336,"style":1694},[1134],[568,3338],{"className":3339,"style":1714},[1713],[568,3341,3342,3345],{"style":3044},[568,3343],{"className":3344,"style":1694},[1134],[568,3346,3348],{"className":3347},[611],[568,3349,1597],{"className":3350},[611],[568,3352,1150],{"className":3353},[1149],[568,3355,3357],{"className":3356},[1122],[568,3358,3361],{"className":3359,"style":3360},[1126],"height:0.686em;",[568,3362],{},[568,3364],{"className":3365},[797,1674],[568,3367],{"className":3368,"style":744},[661],[568,3370,701],{"className":3371},[748],[568,3373],{"className":3374,"style":744},[661],[568,3376,3378,3381],{"className":3377},[602],[568,3379],{"className":3380,"style":676},[606],[568,3382,1597],{"className":3383},[611],[564,3385,3386,3387,3449,3450,3502,3503,3666,3667,3719,3720,3758],{},"Für ",[568,3388,3390,3409],{"className":3389},[571],[568,3391,3393],{"className":3392},[575],[577,3394,3395],{"xmlns":579},[581,3396,3397,3406],{},[584,3398,3399,3401,3403],{},[587,3400,633],{},[635,3402,1591],{},[639,3404,3405],{},"0,001",[591,3407,3408],{"encoding":593},"\\varepsilon = 0{,}001",[568,3410,3412,3430],{"className":3411,"ariaHidden":598},[597],[568,3413,3415,3418,3421,3424,3427],{"className":3414},[602],[568,3416],{"className":3417,"style":607},[606],[568,3419,633],{"className":3420},[611,612],[568,3422],{"className":3423,"style":662},[661],[568,3425,1591],{"className":3426},[666],[568,3428],{"className":3429,"style":662},[661],[568,3431,3433,3436,3439,3445],{"className":3432},[602],[568,3434],{"className":3435,"style":2152},[606],[568,3437,641],{"className":3438},[611],[568,3440,3442],{"className":3441},[611],[568,3443,706],{"className":3444},[765],[568,3446,3448],{"className":3447},[611],"001"," funktioniert ",[568,3451,3453,3472],{"className":3452},[571],[568,3454,3456],{"className":3455},[575],[577,3457,3458],{"xmlns":579},[581,3459,3460,3469],{},[584,3461,3462,3464,3466],{},[587,3463,879],{},[635,3465,1591],{},[639,3467,3468],{},"1000",[591,3470,3471],{"encoding":593},"N = 1000",[568,3473,3475,3493],{"className":3474,"ariaHidden":598},[597],[568,3476,3478,3481,3484,3487,3490],{"className":3477},[602],[568,3479],{"className":3480,"style":891},[606],[568,3482,879],{"className":3483,"style":895},[611,612],[568,3485],{"className":3486,"style":662},[661],[568,3488,1591],{"className":3489},[666],[568,3491],{"className":3492,"style":662},[661],[568,3494,3496,3499],{"className":3495},[602],[568,3497],{"className":3498,"style":676},[606],[568,3500,3468],{"className":3501},[611],": ",[568,3504,3506,3534],{"className":3505},[571],[568,3507,3509],{"className":3508},[575],[577,3510,3511],{"xmlns":579},[581,3512,3513,3531],{},[584,3514,3515,3522,3524,3527,3529],{},[1593,3516,3517,3519],{},[639,3518,1597],{},[639,3520,3521],{},"1001",[635,3523,2240],{},[639,3525,3526],{},"0,000999",[635,3528,1409],{},[639,3530,3405],{},[591,3532,3533],{"encoding":593},"\\frac{1}{1001} \\approx 0{,}000999 \u003C 0{,}001",[568,3535,3537,3620,3648],{"className":3536,"ariaHidden":598},[597],[568,3538,3540,3543,3611,3614,3617],{"className":3539},[602],[568,3541],{"className":3542,"style":1667},[606],[568,3544,3546,3549,3608],{"className":3545},[611],[568,3547],{"className":3548},[737,1674],[568,3550,3552],{"className":3551},[1593],[568,3553,3555,3600],{"className":3554},[1117,1118],[568,3556,3558,3597],{"className":3557},[1122],[568,3559,3561,3575,3583],{"className":3560,"style":1687},[1126],[568,3562,3563,3566],{"style":1690},[568,3564],{"className":3565,"style":1694},[1134],[568,3567,3569],{"className":3568},[1139,1140,1141,1142],[568,3570,3572],{"className":3571},[611,1142],[568,3573,3521],{"className":3574},[611,1142],[568,3576,3577,3580],{"style":1706},[568,3578],{"className":3579,"style":1694},[1134],[568,3581],{"className":3582,"style":1714},[1713],[568,3584,3585,3588],{"style":1717},[568,3586],{"className":3587,"style":1694},[1134],[568,3589,3591],{"className":3590},[1139,1140,1141,1142],[568,3592,3594],{"className":3593},[611,1142],[568,3595,1597],{"className":3596},[611,1142],[568,3598,1150],{"className":3599},[1149],[568,3601,3603],{"className":3602},[1122],[568,3604,3606],{"className":3605,"style":1739},[1126],[568,3607],{},[568,3609],{"className":3610},[797,1674],[568,3612],{"className":3613,"style":662},[661],[568,3615,2240],{"className":3616},[666],[568,3618],{"className":3619,"style":662},[661],[568,3621,3623,3626,3629,3635,3639,3642,3645],{"className":3622},[602],[568,3624],{"className":3625,"style":2152},[606],[568,3627,641],{"className":3628},[611],[568,3630,3632],{"className":3631},[611],[568,3633,706],{"className":3634},[765],[568,3636,3638],{"className":3637},[611],"000999",[568,3640],{"className":3641,"style":662},[661],[568,3643,1409],{"className":3644},[666],[568,3646],{"className":3647,"style":662},[661],[568,3649,3651,3654,3657,3663],{"className":3650},[602],[568,3652],{"className":3653,"style":2152},[606],[568,3655,641],{"className":3656},[611],[568,3658,3660],{"className":3659},[611],[568,3661,706],{"className":3662},[765],[568,3664,3448],{"className":3665},[611],". Für ",[568,3668,3670,3689],{"className":3669},[571],[568,3671,3673],{"className":3672},[575],[577,3674,3675],{"xmlns":579},[581,3676,3677,3686],{},[584,3678,3679,3681,3683],{},[587,3680,1085],{},[635,3682,1591],{},[639,3684,3685],{},"999",[591,3687,3688],{"encoding":593},"n = 999",[568,3690,3692,3710],{"className":3691,"ariaHidden":598},[597],[568,3693,3695,3698,3701,3704,3707],{"className":3694},[602],[568,3696],{"className":3697,"style":607},[606],[568,3699,1085],{"className":3700},[611,612],[568,3702],{"className":3703,"style":662},[661],[568,3705,1591],{"className":3706},[666],[568,3708],{"className":3709,"style":662},[661],[568,3711,3713,3716],{"className":3712},[602],[568,3714],{"className":3715,"style":676},[606],[568,3717,3685],{"className":3718},[611]," ist der Abstand genau ",[568,3721,3723,3737],{"className":3722},[571],[568,3724,3726],{"className":3725},[575],[577,3727,3728],{"xmlns":579},[581,3729,3730,3734],{},[584,3731,3732],{},[639,3733,3405],{},[591,3735,3736],{"encoding":593},"0{,}001",[568,3738,3740],{"className":3739,"ariaHidden":598},[597],[568,3741,3743,3746,3749,3755],{"className":3742},[602],[568,3744],{"className":3745,"style":2152},[606],[568,3747,641],{"className":3748},[611],[568,3750,3752],{"className":3751},[611],[568,3753,706],{"className":3754},[765],[568,3756,3448],{"className":3757},[611]," und damit nicht kleiner.",[564,3760,3761,3901,3902,3905,3906,3934,3935,4055,4056,4084],{},[568,3762,3764,3797],{"className":3763},[571],[568,3765,3767],{"className":3766},[575],[577,3768,3769],{"xmlns":579},[581,3770,3771,3794],{},[584,3772,3773,3779,3781,3783,3785,3787],{},[1079,3774,3775,3777],{},[587,3776,589],{},[587,3778,1085],{},[635,3780,1591],{},[635,3782,696],{"stretchy":695},[635,3784,701],{},[639,3786,1597],{},[3788,3789,3790,3792],"msup",{},[635,3791,720],{"stretchy":695},[587,3793,1085],{},[591,3795,3796],{"encoding":593},"a_n = (-1)^n",[568,3798,3800,3855],{"className":3799,"ariaHidden":598},[597],[568,3801,3803,3806,3846,3849,3852],{"className":3802},[602],[568,3804],{"className":3805,"style":1103},[606],[568,3807,3809,3812],{"className":3808},[611],[568,3810,589],{"className":3811},[611,612],[568,3813,3815],{"className":3814},[1113],[568,3816,3818,3838],{"className":3817},[1117,1118],[568,3819,3821,3835],{"className":3820},[1122],[568,3822,3824],{"className":3823,"style":1127},[1126],[568,3825,3826,3829],{"style":1130},[568,3827],{"className":3828,"style":1135},[1134],[568,3830,3832],{"className":3831},[1139,1140,1141,1142],[568,3833,1085],{"className":3834},[611,612,1142],[568,3836,1150],{"className":3837},[1149],[568,3839,3841],{"className":3840},[1122],[568,3842,3844],{"className":3843,"style":1157},[1126],[568,3845],{},[568,3847],{"className":3848,"style":662},[661],[568,3850,1591],{"className":3851},[666],[568,3853],{"className":3854,"style":662},[661],[568,3856,3858,3861,3864,3867,3870],{"className":3857},[602],[568,3859],{"className":3860,"style":733},[606],[568,3862,696],{"className":3863},[737],[568,3865,701],{"className":3866},[611],[568,3868,1597],{"className":3869},[611],[568,3871,3873,3876],{"className":3872},[797],[568,3874,720],{"className":3875},[797],[568,3877,3879],{"className":3878},[1113],[568,3880,3882],{"className":3881},[1117],[568,3883,3885],{"className":3884},[1122],[568,3886,3889],{"className":3887,"style":3888},[1126],"height:0.6644em;",[568,3890,3892,3895],{"style":3891},"top:-3.063em;margin-right:0.05em;",[568,3893],{"className":3894,"style":1135},[1134],[568,3896,3898],{"className":3897},[1139,1140,1141,1142],[568,3899,1085],{"className":3900},[611,612,1142]," ist ",[615,3903,3904],{},"divergent",": Zwei aufeinanderfolgende Glieder haben immer den Abstand ",[568,3907,3909,3922],{"className":3908},[571],[568,3910,3912],{"className":3911},[575],[577,3913,3914],{"xmlns":579},[581,3915,3916,3920],{},[584,3917,3918],{},[639,3919,2543],{},[591,3921,2543],{"encoding":593},[568,3923,3925],{"className":3924,"ariaHidden":598},[597],[568,3926,3928,3931],{"className":3927},[602],[568,3929],{"className":3930,"style":676},[606],[568,3932,2543],{"className":3933},[611],". Bei ",[568,3936,3938,3960],{"className":3937},[571],[568,3939,3941],{"className":3940},[575],[577,3942,3943],{"xmlns":579},[581,3944,3945,3957],{},[584,3946,3947,3949,3951],{},[587,3948,633],{},[635,3950,1591],{},[1593,3952,3953,3955],{},[639,3954,1597],{},[639,3956,2543],{},[591,3958,3959],{"encoding":593},"\\varepsilon = \\frac{1}{2}",[568,3961,3963,3981],{"className":3962,"ariaHidden":598},[597],[568,3964,3966,3969,3972,3975,3978],{"className":3965},[602],[568,3967],{"className":3968,"style":607},[606],[568,3970,633],{"className":3971},[611,612],[568,3973],{"className":3974,"style":662},[661],[568,3976,1591],{"className":3977},[666],[568,3979],{"className":3980,"style":662},[661],[568,3982,3984,3987],{"className":3983},[602],[568,3985],{"className":3986,"style":1667},[606],[568,3988,3990,3993,4052],{"className":3989},[611],[568,3991],{"className":3992},[737,1674],[568,3994,3996],{"className":3995},[1593],[568,3997,3999,4044],{"className":3998},[1117,1118],[568,4000,4002,4041],{"className":4001},[1122],[568,4003,4005,4019,4027],{"className":4004,"style":1687},[1126],[568,4006,4007,4010],{"style":1690},[568,4008],{"className":4009,"style":1694},[1134],[568,4011,4013],{"className":4012},[1139,1140,1141,1142],[568,4014,4016],{"className":4015},[611,1142],[568,4017,2543],{"className":4018},[611,1142],[568,4020,4021,4024],{"style":1706},[568,4022],{"className":4023,"style":1694},[1134],[568,4025],{"className":4026,"style":1714},[1713],[568,4028,4029,4032],{"style":1717},[568,4030],{"className":4031,"style":1694},[1134],[568,4033,4035],{"className":4034},[1139,1140,1141,1142],[568,4036,4038],{"className":4037},[611,1142],[568,4039,1597],{"className":4040},[611,1142],[568,4042,1150],{"className":4043},[1149],[568,4045,4047],{"className":4046},[1122],[568,4048,4050],{"className":4049,"style":1739},[1126],[568,4051],{},[568,4053],{"className":4054},[797,1674]," könnten nicht beide im Streifen um einen Wert ",[568,4057,4059,4072],{"className":4058},[571],[568,4060,4062],{"className":4061},[575],[577,4063,4064],{"xmlns":579},[581,4065,4066,4070],{},[584,4067,4068],{},[587,4069,589],{},[591,4071,589],{"encoding":593},[568,4073,4075],{"className":4074,"ariaHidden":598},[597],[568,4076,4078,4081],{"className":4077},[602],[568,4079],{"className":4080,"style":607},[606],[568,4082,589],{"className":4083},[611,612]," liegen.",[559,4086,4088],{"id":4087},"typische-fehler","Typische Fehler",[898,4090,4091,4152,4238,4516],{},[901,4092,4093,4094,4122,4123,4151],{},"Die Quantoren vertauschen. „Es gibt ein ",[568,4095,4097,4110],{"className":4096},[571],[568,4098,4100],{"className":4099},[575],[577,4101,4102],{"xmlns":579},[581,4103,4104,4108],{},[584,4105,4106],{},[587,4107,879],{},[591,4109,879],{"encoding":593},[568,4111,4113],{"className":4112,"ariaHidden":598},[597],[568,4114,4116,4119],{"className":4115},[602],[568,4117],{"className":4118,"style":891},[606],[568,4120,879],{"className":4121,"style":895},[611,612],", das für alle ",[568,4124,4126,4139],{"className":4125},[571],[568,4127,4129],{"className":4128},[575],[577,4130,4131],{"xmlns":579},[581,4132,4133,4137],{},[584,4134,4135],{},[587,4136,633],{},[591,4138,948],{"encoding":593},[568,4140,4142],{"className":4141,"ariaHidden":598},[597],[568,4143,4145,4148],{"className":4144},[602],[568,4146],{"className":4147,"style":607},[606],[568,4149,633],{"className":4150},[611,612]," passt“ ist viel stärker und gilt nur für Folgen, die ab einem Index konstant sind.",[901,4153,4154,4155,4183,4184,618,4187,4237],{},"Ein festes ",[568,4156,4158,4171],{"className":4157},[571],[568,4159,4161],{"className":4160},[575],[577,4162,4163],{"xmlns":579},[581,4164,4165,4169],{},[584,4166,4167],{},[587,4168,633],{},[591,4170,948],{"encoding":593},[568,4172,4174],{"className":4173,"ariaHidden":598},[597],[568,4175,4177,4180],{"className":4176},[602],[568,4178],{"className":4179,"style":607},[606],[568,4181,633],{"className":4182},[611,612]," prüfen und daraus Konvergenz folgern. Die Bedingung muss für ",[615,4185,4186],{},"jedes",[568,4188,4190,4207],{"className":4189},[571],[568,4191,4193],{"className":4192},[575],[577,4194,4195],{"xmlns":579},[581,4196,4197,4205],{},[584,4198,4199,4201,4203],{},[587,4200,633],{},[635,4202,637],{},[639,4204,641],{},[591,4206,644],{"encoding":593},[568,4208,4210,4228],{"className":4209,"ariaHidden":598},[597],[568,4211,4213,4216,4219,4222,4225],{"className":4212},[602],[568,4214],{"className":4215,"style":654},[606],[568,4217,633],{"className":4218},[611,612],[568,4220],{"className":4221,"style":662},[661],[568,4223,637],{"className":4224},[666],[568,4226],{"className":4227,"style":662},[661],[568,4229,4231,4234],{"className":4230},[602],[568,4232],{"className":4233,"style":676},[606],[568,4235,641],{"className":4236},[611]," gelten.",[901,4239,4240,4241,4457,4458,4486,4487,4515],{},"Glauben, die Folge müsse sich dem Grenzwert monoton nähern. ",[568,4242,4244,4282],{"className":4243},[571],[568,4245,4247],{"className":4246},[575],[577,4248,4249],{"xmlns":579},[581,4250,4251,4279],{},[584,4252,4253,4259,4261],{},[1079,4254,4255,4257],{},[587,4256,589],{},[587,4258,1085],{},[635,4260,1591],{},[1593,4262,4263,4277],{},[584,4264,4265,4267,4269,4271],{},[635,4266,696],{"stretchy":695},[635,4268,701],{},[639,4270,1597],{},[3788,4272,4273,4275],{},[635,4274,720],{"stretchy":695},[587,4276,1085],{},[587,4278,1085],{},[591,4280,4281],{"encoding":593},"a_n = \\frac{(-1)^n}{n}",[568,4283,4285,4340],{"className":4284,"ariaHidden":598},[597],[568,4286,4288,4291,4331,4334,4337],{"className":4287},[602],[568,4289],{"className":4290,"style":1103},[606],[568,4292,4294,4297],{"className":4293},[611],[568,4295,589],{"className":4296},[611,612],[568,4298,4300],{"className":4299},[1113],[568,4301,4303,4323],{"className":4302},[1117,1118],[568,4304,4306,4320],{"className":4305},[1122],[568,4307,4309],{"className":4308,"style":1127},[1126],[568,4310,4311,4314],{"style":1130},[568,4312],{"className":4313,"style":1135},[1134],[568,4315,4317],{"className":4316},[1139,1140,1141,1142],[568,4318,1085],{"className":4319},[611,612,1142],[568,4321,1150],{"className":4322},[1149],[568,4324,4326],{"className":4325},[1122],[568,4327,4329],{"className":4328,"style":1157},[1126],[568,4330],{},[568,4332],{"className":4333,"style":662},[661],[568,4335,1591],{"className":4336},[666],[568,4338],{"className":4339,"style":662},[661],[568,4341,4343,4347],{"className":4342},[602],[568,4344],{"className":4345,"style":4346},[606],"height:1.355em;vertical-align:-0.345em;",[568,4348,4350,4353,4454],{"className":4349},[611],[568,4351],{"className":4352},[737,1674],[568,4354,4356],{"className":4355},[1593],[568,4357,4359,4446],{"className":4358},[1117,1118],[568,4360,4362,4443],{"className":4361},[1122],[568,4363,4366,4380,4388],{"className":4364,"style":4365},[1126],"height:1.01em;",[568,4367,4368,4371],{"style":1690},[568,4369],{"className":4370,"style":1694},[1134],[568,4372,4374],{"className":4373},[1139,1140,1141,1142],[568,4375,4377],{"className":4376},[611,1142],[568,4378,1085],{"className":4379},[611,612,1142],[568,4381,4382,4385],{"style":1706},[568,4383],{"className":4384,"style":1694},[1134],[568,4386],{"className":4387,"style":1714},[1713],[568,4389,4391,4394],{"style":4390},"top:-3.485em;",[568,4392],{"className":4393,"style":1694},[1134],[568,4395,4397],{"className":4396},[1139,1140,1141,1142],[568,4398,4400,4403,4406,4409],{"className":4399},[611,1142],[568,4401,696],{"className":4402},[737,1142],[568,4404,701],{"className":4405},[611,1142],[568,4407,1597],{"className":4408},[611,1142],[568,4410,4412,4415],{"className":4411},[797,1142],[568,4413,720],{"className":4414},[797,1142],[568,4416,4418],{"className":4417},[1113],[568,4419,4421],{"className":4420},[1117],[568,4422,4424],{"className":4423},[1122],[568,4425,4428],{"className":4426,"style":4427},[1126],"height:0.7385em;",[568,4429,4431,4435],{"style":4430},"top:-2.931em;margin-right:0.0714em;",[568,4432],{"className":4433,"style":4434},[1134],"height:2.5em;",[568,4436,4440],{"className":4437},[1139,4438,4439,1142],"reset-size3","size1",[568,4441,1085],{"className":4442},[611,612,1142],[568,4444,1150],{"className":4445},[1149],[568,4447,4449],{"className":4448},[1122],[568,4450,4452],{"className":4451,"style":1739},[1126],[568,4453],{},[568,4455],{"className":4456},[797,1674]," springt um ",[568,4459,4461,4474],{"className":4460},[571],[568,4462,4464],{"className":4463},[575],[577,4465,4466],{"xmlns":579},[581,4467,4468,4472],{},[584,4469,4470],{},[639,4471,641],{},[591,4473,641],{"encoding":593},[568,4475,4477],{"className":4476,"ariaHidden":598},[597],[568,4478,4480,4483],{"className":4479},[602],[568,4481],{"className":4482,"style":676},[606],[568,4484,641],{"className":4485},[611]," herum und konvergiert trotzdem gegen ",[568,4488,4490,4503],{"className":4489},[571],[568,4491,4493],{"className":4492},[575],[577,4494,4495],{"xmlns":579},[581,4496,4497,4501],{},[584,4498,4499],{},[639,4500,641],{},[591,4502,641],{"encoding":593},[568,4504,4506],{"className":4505,"ariaHidden":598},[597],[568,4507,4509,4512],{"className":4508},[602],[568,4510],{"className":4511,"style":676},[606],[568,4513,641],{"className":4514},[611],".",[901,4517,4518,4563,4564,4607,4608,4636],{},[568,4519,4521,4538],{"className":4520},[571],[568,4522,4524],{"className":4523},[575],[577,4525,4526],{"xmlns":579},[581,4527,4528,4535],{},[584,4529,4530,4533],{},[635,4531,4532],{},"≤",[587,4534,633],{},[591,4536,4537],{"encoding":593},"\\leq \\varepsilon",[568,4539,4541,4554],{"className":4540,"ariaHidden":598},[597],[568,4542,4544,4548,4551],{"className":4543},[602],[568,4545],{"className":4546,"style":4547},[606],"height:0.7719em;vertical-align:-0.136em;",[568,4549,4532],{"className":4550},[666],[568,4552],{"className":4553,"style":662},[661],[568,4555,4557,4560],{"className":4556},[602],[568,4558],{"className":4559,"style":607},[606],[568,4561,633],{"className":4562},[611,612]," und ",[568,4565,4567,4583],{"className":4566},[571],[568,4568,4570],{"className":4569},[575],[577,4571,4572],{"xmlns":579},[581,4573,4574,4580],{},[584,4575,4576,4578],{},[635,4577,1409],{},[587,4579,633],{},[591,4581,4582],{"encoding":593},"\u003C \\varepsilon",[568,4584,4586,4598],{"className":4585,"ariaHidden":598},[597],[568,4587,4589,4592,4595],{"className":4588},[602],[568,4590],{"className":4591,"style":654},[606],[568,4593,1409],{"className":4594},[666],[568,4596],{"className":4597,"style":662},[661],[568,4599,4601,4604],{"className":4600},[602],[568,4602],{"className":4603,"style":607},[606],[568,4605,633],{"className":4606},[611,612]," für wesentlich halten. Beide Varianten definieren denselben Grenzwertbegriff, nur das konkrete ",[568,4609,4611,4624],{"className":4610},[571],[568,4612,4614],{"className":4613},[575],[577,4615,4616],{"xmlns":579},[581,4617,4618,4622],{},[584,4619,4620],{},[587,4621,879],{},[591,4623,879],{"encoding":593},[568,4625,4627],{"className":4626,"ariaHidden":598},[597],[568,4628,4630,4633],{"className":4629},[602],[568,4631],{"className":4632,"style":891},[606],[568,4634,879],{"className":4635,"style":895},[611,612]," verschiebt sich eventuell um eins.",{"title":4638,"searchDepth":4639,"depth":4639,"links":4640},"",2,[4641,4642,4643],{"id":561,"depth":4639,"text":562},{"id":1567,"depth":4639,"text":1568},{"id":4087,"depth":4639,"text":4088},[4645,4648,4651,4654,4657,4660],{"lhs":4646,"rhs":4647},"round(1\u002F101, 6)","0.009901",{"lhs":4649,"rhs":4650},"1\u002F100","0.01",{"lhs":4652,"rhs":4653},"(2*n + 1)\u002F(n + 1) - 2","-1\u002F(n + 1)",{"lhs":4655,"rhs":4656},"1\u002F(999 + 1)","0.001",{"lhs":4658,"rhs":4659},"round(1\u002F(1000 + 1), 7)","0.0009990",{"lhs":4661,"rhs":2543,"where":4662},"abs((-1)^n - (-1)^(n + 1))",{"n":4663},5,"(a_n) \\text{ reelle Folge},\\ a \\in \\mathbb{R}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\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=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">reelle\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">Folge\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">,\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:0.3em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a \\in \\mathbb{R}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6889em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md",{"caption":4669,"x":4670,"y":4673,"unit":4676,"unitY":4677,"items":4678},"Die Glieder aₙ = (2n + 1)\u002F(n + 1) nähern sich dem Grenzwert a = 2; für ε = 0,25 liegen ab N = 4 alle Glieder näher als ε an a",[4671,4672],0,15,[4674,4675],1.25,2.45,18,200,[4679,4687,4693,4697,4700,4704,4709,4712,4715,4718,4721,4725,4729,4733,4737,4741,4745,4749,4754,4756,4759,4762,4764],{"type":4680,"from":4681,"to":4684,"style":4686},"segment",[4682,4683],0.3,1.35,[4685,4683],13,"muted",{"type":4680,"from":4688,"to":4690,"style":4692},[4689,4683],4,[4689,4691],2.25,"dashed",{"type":4680,"from":4694,"to":4695,"style":4692},[4682,4691],[4696,4691],12.3,{"type":4680,"from":4698,"to":4699,"style":4686},[4682,4639],[4696,4639],{"type":4680,"from":4701,"to":4703,"style":4692},[4682,4702],1.75,[4696,4702],{"type":4705,"at":4706},"point",[4707,4708],1,1.5,{"type":4705,"at":4710},[4639,4711],1.6667,{"type":4705,"at":4713},[4714,4702],3,{"type":4705,"at":4716},[4689,4717],1.8,{"type":4705,"at":4719},[4663,4720],1.8333,{"type":4705,"at":4722},[4723,4724],6,1.8571,{"type":4705,"at":4726},[4727,4728],7,1.875,{"type":4705,"at":4730},[4731,4732],8,1.8889,{"type":4705,"at":4734},[4735,4736],9,1.9,{"type":4705,"at":4738},[4739,4740],10,1.9091,{"type":4705,"at":4742},[4743,4744],11,1.9167,{"type":4705,"at":4746},[4747,4748],12,1.9231,{"type":4750,"at":4751,"text":4753},"label",[4752,4691],13.9,"a + ε",{"type":4750,"at":4755,"text":589},[4752,4639],{"type":4750,"at":4757,"text":4758},[4752,4702],"a − ε",{"type":4750,"at":4760,"text":1597},[4707,4761],1.29,{"type":4750,"at":4763,"text":879},[4689,4761],{"type":4750,"at":4765,"text":1085},[4766,4683],13.6,"\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 270 240\" width=\"270\" height=\"240\" role=\"img\" aria-label=\"Die Glieder aₙ = (2n + 1)\u002F(n + 1) nähern sich dem Grenzwert a = 2; für ε = 0,25 liegen ab N = 4 alle Glieder näher als ε an a\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-limit-definition-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-limit-definition-clip\">\u003Crect x=\"0\" y=\"0\" width=\"270\" height=\"240\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cline x1=\"5.4\" y1=\"220\" x2=\"234\" y2=\"220\" class=\"fig-muted\"\u002F>\u003Cline x1=\"72\" y1=\"220\" x2=\"72\" y2=\"40\" class=\"fig-dashed\"\u002F>\u003Cline x1=\"5.4\" y1=\"40\" x2=\"221.4\" y2=\"40\" class=\"fig-dashed\"\u002F>\u003Cline x1=\"5.4\" y1=\"90\" x2=\"221.4\" y2=\"90\" class=\"fig-muted\"\u002F>\u003Cline x1=\"5.4\" y1=\"140\" x2=\"221.4\" y2=\"140\" class=\"fig-dashed\"\u002F>\u003Ccircle cx=\"18\" cy=\"190\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"36\" cy=\"156.66\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"54\" cy=\"140\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"72\" cy=\"130\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"90\" cy=\"123.34\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"108\" cy=\"118.58\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"126\" cy=\"115\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"144\" cy=\"112.22\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"162\" cy=\"110\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"180\" cy=\"108.18\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"198\" cy=\"106.66\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ccircle cx=\"216\" cy=\"105.38\" r=\"3\" class=\"fig-dot\"\u002F>\u003Ctext x=\"250.2\" y=\"40\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a + ε\u003C\u002Ftext>\u003Ctext x=\"250.2\" y=\"90\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a\u003C\u002Ftext>\u003Ctext x=\"250.2\" y=\"140\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">a − ε\u003C\u002Ftext>\u003Ctext x=\"18\" y=\"232\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">1\u003C\u002Ftext>\u003Ctext x=\"72\" y=\"232\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">N\u003C\u002Ftext>\u003Ctext x=\"244.8\" y=\"220\" text-anchor=\"middle\" dominant-baseline=\"middle\" class=\"fig-label\">n\u003C\u002Ftext>\u003C\u002Fsvg>","limit-definition","\\lim_{n \\to \\infty} a_n = a \\;\\Leftrightarrow\\; \\forall \\varepsilon > 0\\ \\exists N \\in \\mathbb{N}\\ \\forall n \\geq N:\\ |a_n - a| \u003C \\varepsilon","\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>\u003Cmunder>\u003Cmrow>\u003Cmi>lim\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>→\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmunder>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⇔\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmi mathvariant=\"normal\">∀\u003C\u002Fmi>\u003Cmi>ε\u003C\u002Fmi>\u003Cmo>>\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi mathvariant=\"normal\">∃\u003C\u002Fmi>\u003Cmi>N\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">N\u003C\u002Fmi>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi mathvariant=\"normal\">∀\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmi>N\u003C\u002Fmi>\u003Cmo>:\u003C\u002Fmo>\u003Cmtext> \u003C\u002Fmtext>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmo><\u003C\u002Fmo>\u003Cmi>ε\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\lim_{n \\to \\infty} a_n = a \\;\\Leftrightarrow\\; \\forall \\varepsilon > 0\\ \\exists N \\in \\mathbb{N}\\ \\forall n \\geq N:\\ |a_n - a| < \\varepsilon\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:1.3944em;vertical-align:-0.7em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6944em;\">\u003Cspan style=\"top:-2.4em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\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\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop\">lim\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:0.7em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"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=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">⇔\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7335em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∀\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">ε\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:0.7335em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mspace\"> \u003C\u002Fspan>\u003Cspan class=\"mord\">∃\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.109em;\">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:0.8304em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">N\u003C\u002Fspan>\u003Cspan class=\"mspace\"> \u003C\u002Fspan>\u003Cspan class=\"mord\">∀\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>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">:\u003C\u002Fspan>\u003Cspan class=\"mspace\"> \u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"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=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord 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