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Allgemeiner gilt für jede reelle Zahl ",[568,1100,1102,1115],{"className":1101},[571],[568,1103,1105],{"className":1104},[575],[577,1106,1107],{"xmlns":579},[581,1108,1109,1113],{},[584,1110,1111],{},[609,1112,1009],{},[618,1114,1009],{"encoding":620},[568,1116,1118],{"className":1117,"ariaHidden":594},[625],[568,1119,1121,1124],{"className":1120},[629],[568,1122],{"className":1123,"style":818},[633],[568,1125,1009],{"className":1126},[656,714],":",[568,1129,1132],{"className":1130},[1131],"katex-display",[568,1133,1135,1198],{"className":1134},[571],[568,1136,1138],{"className":1137},[575],[577,1139,1141],{"xmlns":579,"display":1140},"block",[581,1142,1143,1195],{},[584,1144,1145,1151,1154,1175],{},[587,1146,1147,1149],{},[609,1148,873],{},[609,1150,1009],{},[592,1152,1153],{},"=",[1155,1156,1157,1164],"munder",{},[584,1158,1159,1162],{},[609,1160,1161],{},"lim",[592,1163,1071],{},[584,1165,1166,1168,1171],{},[609,1167,611],{},[592,1169,1170],{},"→",[609,1172,1174],{"mathvariant":1173},"normal","∞",[587,1176,1177,1193],{},[584,1178,1179,1181,1183,1185,1191],{},[592,1180,595],{"fence":594},[597,1182,599],{},[592,1184,602],{},[604,1186,1187,1189],{},[609,1188,1009],{},[609,1190,611],{},[592,1192,614],{"fence":594},[609,1194,611],{},[618,1196,1197],{"encoding":620},"e^x = \\lim_{n \\to \\infty} \\left( 1 + \\frac{x}{n} \\right)^n",[568,1199,1201,1247],{"className":1200,"ariaHidden":594},[625],[568,1202,1204,1208,1238,1241,1244],{"className":1203},[629],[568,1205],{"className":1206,"style":1207},[633],"height:0.7144em;",[568,1209,1211,1214],{"className":1210},[656],[568,1212,873],{"className":1213},[656,714],[568,1215,1217],{"className":1216},[768],[568,1218,1220],{"className":1219},[682],[568,1221,1223],{"className":1222},[687],[568,1224,1226],{"className":1225,"style":1207},[691],[568,1227,1229,1232],{"style":1228},"top:-3.113em;margin-right:0.05em;",[568,1230],{"className":1231,"style":785},[699],[568,1233,1235],{"className":1234},[704,705,706,707],[568,1236,1009],{"className":1237},[656,714,707],[568,1239],{"className":1240,"style":899},[660],[568,1242,1153],{"className":1243},[903],[568,1245],{"className":1246,"style":899},[660],[568,1248,1250,1254,1311,1314],{"className":1249},[629],[568,1251],{"className":1252,"style":1253},[633],"height:1.9043em;vertical-align:-0.7em;",[568,1255,1258],{"className":1256},[1090,1257],"op-limits",[568,1259,1261,1302],{"className":1260},[682,683],[568,1262,1264,1299],{"className":1263},[687],[568,1265,1267,1288],{"className":1266,"style":1086},[691],[568,1268,1270,1273],{"style":1269},"top:-2.4em;margin-left:0em;",[568,1271],{"className":1272,"style":700},[699],[568,1274,1276],{"className":1275},[704,705,706,707],[568,1277,1279,1282,1285],{"className":1278},[656,707],[568,1280,611],{"className":1281},[656,714,707],[568,1283,1170],{"className":1284},[903,707],[568,1286,1174],{"className":1287},[656,707],[568,1289,1291,1294],{"style":1290},"top:-3em;",[568,1292],{"className":1293,"style":700},[699],[568,1295,1296],{},[568,1297,1161],{"className":1298},[1090],[568,1300,745],{"className":1301},[744],[568,1303,1305],{"className":1304},[687],[568,1306,1309],{"className":1307,"style":1308},[691],"height:0.7em;",[568,1310],{},[568,1312],{"className":1313,"style":1094},[660],[568,1315,1317,1411],{"className":1316},[638],[568,1318,1320,1327,1330,1333,1336,1339,1405],{"className":1319},[638],[568,1321,1323],{"className":1322,"style":647},[645,646],[568,1324,595],{"className":1325},[651,1326],"size2",[568,1328,599],{"className":1329},[656],[568,1331],{"className":1332,"style":661},[660],[568,1334,602],{"className":1335},[665],[568,1337],{"className":1338,"style":661},[660],[568,1340,1342,1345,1402],{"className":1341},[656],[568,1343],{"className":1344},[645,675],[568,1346,1348],{"className":1347},[604],[568,1349,1351,1393],{"className":1350},[682,683],[568,1352,1354,1390],{"className":1353},[687],[568,1355,1358,1370,1378],{"className":1356,"style":1357},[691],"height:1.1076em;",[568,1359,1361,1364],{"style":1360},"top:-2.314em;",[568,1362],{"className":1363,"style":700},[699],[568,1365,1367],{"className":1366},[656],[568,1368,611],{"className":1369},[656,714],[568,1371,1372,1375],{"style":717},[568,1373],{"className":1374,"style":700},[699],[568,1376],{"className":1377,"style":725},[724],[568,1379,1381,1384],{"style":1380},"top:-3.677em;",[568,1382],{"className":1383,"style":700},[699],[568,1385,1387],{"className":1386},[656],[568,1388,1009],{"className":1389},[656,714],[568,1391,745],{"className":1392},[744],[568,1394,1396],{"className":1395},[687],[568,1397,1400],{"className":1398,"style":1399},[691],"height:0.686em;",[568,1401],{},[568,1403],{"className":1404},[758,675],[568,1406,1408],{"className":1407,"style":647},[758,646],[568,1409,614],{"className":1410},[651,1326],[568,1412,1414],{"className":1413},[768],[568,1415,1417],{"className":1416},[682],[568,1418,1420],{"className":1419},[687],[568,1421,1424],{"className":1422,"style":1423},[691],"height:1.2043em;",[568,1425,1427,1430],{"style":1426},"top:-3.6029em;margin-right:0.05em;",[568,1428],{"className":1429,"style":785},[699],[568,1431,1433],{"className":1432},[704,705,706,707],[568,1434,611],{"className":1435},[656,714,707],[564,1437,1438,1439,1483,1484,1512,1513,1622,1623,1787,1788,1791,1792,1820],{},"Eine anschauliche Deutung liefert die Verzinsung: Wird ein Betrag zu ",[568,1440,1442,1464],{"className":1441},[571],[568,1443,1445],{"className":1444},[575],[577,1446,1447],{"xmlns":579},[581,1448,1449,1461],{},[584,1450,1451,1454,1458],{},[597,1452,1453],{},"100",[1455,1456,1457],"mtext",{}," ",[609,1459,1460],{"mathvariant":1173},"%",[618,1462,1463],{"encoding":620},"100\\,\\%",[568,1465,1467],{"className":1466,"ariaHidden":594},[625],[568,1468,1470,1474,1477,1480],{"className":1469},[629],[568,1471],{"className":1472,"style":1473},[633],"height:0.8056em;vertical-align:-0.0556em;",[568,1475,1453],{"className":1476},[656],[568,1478],{"className":1479,"style":1094},[660],[568,1481,1460],{"className":1482},[656]," pro Jahr verzinst, aber in ",[568,1485,1487,1500],{"className":1486},[571],[568,1488,1490],{"className":1489},[575],[577,1491,1492],{"xmlns":579},[581,1493,1494,1498],{},[584,1495,1496],{},[609,1497,611],{},[618,1499,611],{"encoding":620},[568,1501,1503],{"className":1502,"ariaHidden":594},[625],[568,1504,1506,1509],{"className":1505},[629],[568,1507],{"className":1508,"style":818},[633],[568,1510,611],{"className":1511},[656,714]," gleich langen Abschnitten mit je ",[568,1514,1516,1538],{"className":1515},[571],[568,1517,1519],{"className":1518},[575],[577,1520,1521],{"xmlns":579},[581,1522,1523,1535],{},[584,1524,1525,1531,1533],{},[604,1526,1527,1529],{},[597,1528,1453],{},[609,1530,611],{},[1455,1532,1457],{},[609,1534,1460],{"mathvariant":1173},[618,1536,1537],{"encoding":620},"\\frac{100}{n}\\,\\%",[568,1539,1541],{"className":1540,"ariaHidden":594},[625],[568,1542,1544,1548,1616,1619],{"className":1543},[629],[568,1545],{"className":1546,"style":1547},[633],"height:1.1901em;vertical-align:-0.345em;",[568,1549,1551,1554,1613],{"className":1550},[656],[568,1552],{"className":1553},[645,675],[568,1555,1557],{"className":1556},[604],[568,1558,1560,1605],{"className":1559},[682,683],[568,1561,1563,1602],{"className":1562},[687],[568,1564,1566,1580,1588],{"className":1565,"style":692},[691],[568,1567,1568,1571],{"style":695},[568,1569],{"className":1570,"style":700},[699],[568,1572,1574],{"className":1573},[704,705,706,707],[568,1575,1577],{"className":1576},[656,707],[568,1578,611],{"className":1579},[656,714,707],[568,1581,1582,1585],{"style":717},[568,1583],{"className":1584,"style":700},[699],[568,1586],{"className":1587,"style":725},[724],[568,1589,1590,1593],{"style":728},[568,1591],{"className":1592,"style":700},[699],[568,1594,1596],{"className":1595},[704,705,706,707],[568,1597,1599],{"className":1598},[656,707],[568,1600,1453],{"className":1601},[656,707],[568,1603,745],{"className":1604},[744],[568,1606,1608],{"className":1607},[687],[568,1609,1611],{"className":1610,"style":752},[691],[568,1612],{},[568,1614],{"className":1615},[758,675],[568,1617],{"className":1618,"style":1094},[660],[568,1620,1460],{"className":1621},[656],", wächst er in einem Jahr auf das ",[568,1624,1626,1657],{"className":1625},[571],[568,1627,1629],{"className":1628},[575],[577,1630,1631],{"xmlns":579},[581,1632,1633,1655],{},[584,1634,1635],{},[587,1636,1637,1653],{},[584,1638,1639,1641,1643,1645,1651],{},[592,1640,595],{"fence":594},[597,1642,599],{},[592,1644,602],{},[604,1646,1647,1649],{},[597,1648,599],{},[609,1650,611],{},[592,1652,614],{"fence":594},[609,1654,611],{},[618,1656,621],{"encoding":620},[568,1658,1660],{"className":1659,"ariaHidden":594},[625],[568,1661,1663,1666],{"className":1662},[629],[568,1664],{"className":1665,"style":634},[633],[568,1667,1669,1764],{"className":1668},[638],[568,1670,1672,1678,1681,1684,1687,1690,1758],{"className":1671},[638],[568,1673,1675],{"className":1674,"style":647},[645,646],[568,1676,595],{"className":1677},[651,652],[568,1679,599],{"className":1680},[656],[568,1682],{"className":1683,"style":661},[660],[568,1685,602],{"className":1686},[665],[568,1688],{"className":1689,"style":661},[660],[568,1691,1693,1696,1755],{"className":1692},[656],[568,1694],{"className":1695},[645,675],[568,1697,1699],{"className":1698},[604],[568,1700,1702,1747],{"className":1701},[682,683],[568,1703,1705,1744],{"className":1704},[687],[568,1706,1708,1722,1730],{"className":1707,"style":692},[691],[568,1709,1710,1713],{"style":695},[568,1711],{"className":1712,"style":700},[699],[568,1714,1716],{"className":1715},[704,705,706,707],[568,1717,1719],{"className":1718},[656,707],[568,1720,611],{"className":1721},[656,714,707],[568,1723,1724,1727],{"style":717},[568,1725],{"className":1726,"style":700},[699],[568,1728],{"className":1729,"style":725},[724],[568,1731,1732,1735],{"style":728},[568,1733],{"className":1734,"style":700},[699],[568,1736,1738],{"className":1737},[704,705,706,707],[568,1739,1741],{"className":1740},[656,707],[568,1742,599],{"className":1743},[656,707],[568,1745,745],{"className":1746},[744],[568,1748,1750],{"className":1749},[687],[568,1751,1753],{"className":1752,"style":752},[691],[568,1754],{},[568,1756],{"className":1757},[758,675],[568,1759,1761],{"className":1760,"style":647},[758,646],[568,1762,614],{"className":1763},[651,652],[568,1765,1767],{"className":1766},[768],[568,1768,1770],{"className":1769},[682],[568,1771,1773],{"className":1772},[687],[568,1774,1776],{"className":1775,"style":778},[691],[568,1777,1778,1781],{"style":781},[568,1779],{"className":1780,"style":785},[699],[568,1782,1784],{"className":1783},[704,705,706,707],[568,1785,611],{"className":1786},[656,714,707],"-Fache. Bei immer feinerer Unterteilung (",[855,1789,1790],{},"stetige Verzinsung",") wird daraus das ",[568,1793,1795,1808],{"className":1794},[571],[568,1796,1798],{"className":1797},[575],[577,1799,1800],{"xmlns":579},[581,1801,1802,1806],{},[584,1803,1804],{},[609,1805,873],{},[618,1807,873],{"encoding":620},[568,1809,1811],{"className":1810,"ariaHidden":594},[625],[568,1812,1814,1817],{"className":1813},[629],[568,1815],{"className":1816,"style":818},[633],[568,1818,873],{"className":1819},[656,714],"-Fache.",[559,1822,1824],{"id":1823},"beispiele","Beispiele",[564,1826,1827,1828,1856],{},"Die ersten Werte der Folge nähern sich ",[568,1829,1831,1844],{"className":1830},[571],[568,1832,1834],{"className":1833},[575],[577,1835,1836],{"xmlns":579},[581,1837,1838,1842],{},[584,1839,1840],{},[609,1841,873],{},[618,1843,873],{"encoding":620},[568,1845,1847],{"className":1846,"ariaHidden":594},[625],[568,1848,1850,1853],{"className":1849},[629],[568,1851],{"className":1852,"style":818},[633],[568,1854,873],{"className":1855},[656,714]," nur langsam:",[568,1858,1860],{"className":1859},[1131],[568,1861,1863,2068],{"className":1862},[571],[568,1864,1866],{"className":1865},[575],[577,1867,1868],{"xmlns":579,"display":1140},[581,1869,1870,2065],{},[1871,1872,1876,1909,1938,1970,2002,2033],"mtable",{"rowspacing":1873,"columnalign":1874,"columnspacing":1875},"0.25em","right left","0em",[1877,1878,1879,1894],"mtr",{},[1880,1881,1882],"mtd",{},[1883,1884,1886],"mstyle",{"scriptlevel":1885,"displaystyle":594},"0",[584,1887,1888,1890,1892],{},[609,1889,611],{},[592,1891,1153],{},[597,1893,599],{},[1880,1895,1896],{},[1883,1897,1898],{"scriptlevel":1885,"displaystyle":594},[584,1899,1900,1902,1904,1907],{},[584,1901],{},[592,1903,1127],{},[660,1905],{"width":1906},"1em",[597,1908,917],{},[1877,1910,1911,1923],{},[1880,1912,1913],{},[1883,1914,1915],{"scriptlevel":1885,"displaystyle":594},[584,1916,1917,1919,1921],{},[609,1918,611],{},[592,1920,1153],{},[597,1922,917],{},[1880,1924,1925],{},[1883,1926,1927],{"scriptlevel":1885,"displaystyle":594},[584,1928,1929,1931,1933,1935],{},[584,1930],{},[592,1932,1127],{},[660,1934],{"width":1906},[597,1936,1937],{},"2,25",[1877,1939,1940,1953],{},[1880,1941,1942],{},[1883,1943,1944],{"scriptlevel":1885,"displaystyle":594},[584,1945,1946,1948,1950],{},[609,1947,611],{},[592,1949,1153],{},[597,1951,1952],{},"10",[1880,1954,1955],{},[1883,1956,1957],{"scriptlevel":1885,"displaystyle":594},[584,1958,1959,1961,1963,1965,1967],{},[584,1960],{},[592,1962,1127],{},[660,1964],{"width":1906},[592,1966,876],{},[597,1968,1969],{},"2,5937",[1877,1971,1972,1985],{},[1880,1973,1974],{},[1883,1975,1976],{"scriptlevel":1885,"displaystyle":594},[584,1977,1978,1980,1982],{},[609,1979,611],{},[592,1981,1153],{},[597,1983,1984],{},"12",[1880,1986,1987],{},[1883,1988,1989],{"scriptlevel":1885,"displaystyle":594},[584,1990,1991,1993,1995,1997,1999],{},[584,1992],{},[592,1994,1127],{},[660,1996],{"width":1906},[592,1998,876],{},[597,2000,2001],{},"2,6130",[1877,2003,2004,2016],{},[1880,2005,2006],{},[1883,2007,2008],{"scriptlevel":1885,"displaystyle":594},[584,2009,2010,2012,2014],{},[609,2011,611],{},[592,2013,1153],{},[597,2015,1453],{},[1880,2017,2018],{},[1883,2019,2020],{"scriptlevel":1885,"displaystyle":594},[584,2021,2022,2024,2026,2028,2030],{},[584,2023],{},[592,2025,1127],{},[660,2027],{"width":1906},[592,2029,876],{},[597,2031,2032],{},"2,7048",[1877,2034,2035,2048],{},[1880,2036,2037],{},[1883,2038,2039],{"scriptlevel":1885,"displaystyle":594},[584,2040,2041,2043,2045],{},[609,2042,611],{},[592,2044,1153],{},[597,2046,2047],{},"1000",[1880,2049,2050],{},[1883,2051,2052],{"scriptlevel":1885,"displaystyle":594},[584,2053,2054,2056,2058,2060,2062],{},[584,2055],{},[592,2057,1127],{},[660,2059],{"width":1906},[592,2061,876],{},[597,2063,2064],{},"2,7169",[618,2066,2067],{"encoding":620},"\\begin{aligned}\nn = 1&: \\quad 2 \\\\\nn = 2&: \\quad 2{,}25 \\\\\nn = 10&: \\quad \\approx 2{,}5937 \\\\\nn = 12&: \\quad \\approx 2{,}6130 \\\\\nn = 100&: \\quad \\approx 2{,}7048 \\\\\nn = 1000&: \\quad \\approx 2{,}7169\n\\end{aligned}",[568,2069,2071],{"className":2070,"ariaHidden":594},[625],[568,2072,2074,2078],{"className":2073},[629],[568,2075],{"className":2076,"style":2077},[633],"height:8.7em;vertical-align:-4.1em;",[568,2079,2081],{"className":2080},[656],[568,2082,2084,2254],{"className":2083},[1871],[568,2085,2088],{"className":2086},[2087],"col-align-r",[568,2089,2091,2245],{"className":2090},[682,683],[568,2092,2094,2242],{"className":2093},[687],[568,2095,2098,2122,2146,2170,2194,2218],{"className":2096,"style":2097},[691],"height:4.6em;",[568,2099,2101,2104],{"style":2100},"top:-6.76em;",[568,2102],{"className":2103,"style":700},[699],[568,2105,2107,2110,2113,2116,2119],{"className":2106},[656],[568,2108,611],{"className":2109},[656,714],[568,2111],{"className":2112,"style":899},[660],[568,2114,1153],{"className":2115},[903],[568,2117],{"className":2118,"style":899},[660],[568,2120,599],{"className":2121},[656],[568,2123,2125,2128],{"style":2124},"top:-5.26em;",[568,2126],{"className":2127,"style":700},[699],[568,2129,2131,2134,2137,2140,2143],{"className":2130},[656],[568,2132,611],{"className":2133},[656,714],[568,2135],{"className":2136,"style":899},[660],[568,2138,1153],{"className":2139},[903],[568,2141],{"className":2142,"style":899},[660],[568,2144,917],{"className":2145},[656],[568,2147,2149,2152],{"style":2148},"top:-3.76em;",[568,2150],{"className":2151,"style":700},[699],[568,2153,2155,2158,2161,2164,2167],{"className":2154},[656],[568,2156,611],{"className":2157},[656,714],[568,2159],{"className":2160,"style":899},[660],[568,2162,1153],{"className":2163},[903],[568,2165],{"className":2166,"style":899},[660],[568,2168,1952],{"className":2169},[656],[568,2171,2173,2176],{"style":2172},"top:-2.26em;",[568,2174],{"className":2175,"style":700},[699],[568,2177,2179,2182,2185,2188,2191],{"className":2178},[656],[568,2180,611],{"className":2181},[656,714],[568,2183],{"className":2184,"style":899},[660],[568,2186,1153],{"className":2187},[903],[568,2189],{"className":2190,"style":899},[660],[568,2192,1984],{"className":2193},[656],[568,2195,2197,2200],{"style":2196},"top:-0.76em;",[568,2198],{"className":2199,"style":700},[699],[568,2201,2203,2206,2209,2212,2215],{"className":2202},[656],[568,2204,611],{"className":2205},[656,714],[568,2207],{"className":2208,"style":899},[660],[568,2210,1153],{"className":2211},[903],[568,2213],{"className":2214,"style":899},[660],[568,2216,1453],{"className":2217},[656],[568,2219,2221,2224],{"style":2220},"top:0.74em;",[568,2222],{"className":2223,"style":700},[699],[568,2225,2227,2230,2233,2236,2239],{"className":2226},[656],[568,2228,611],{"className":2229},[656,714],[568,2231],{"className":2232,"style":899},[660],[568,2234,1153],{"className":2235},[903],[568,2237],{"className":2238,"style":899},[660],[568,2240,2047],{"className":2241},[656],[568,2243,745],{"className":2244},[744],[568,2246,2248],{"className":2247},[687],[568,2249,2252],{"className":2250,"style":2251},[691],"height:4.1em;",[568,2253],{},[568,2255,2258],{"className":2256},[2257],"col-align-l",[568,2259,2261,2489],{"className":2260},[682,683],[568,2262,2264,2486],{"className":2263},[687],[568,2265,2267,2294,2330,2369,2408,2447],{"className":2266,"style":2097},[691],[568,2268,2269,2272],{"style":2100},[568,2270],{"className":2271,"style":700},[699],[568,2273,2275,2278,2281,2284,2288,2291],{"className":2274},[656],[568,2276],{"className":2277},[656],[568,2279],{"className":2280,"style":899},[660],[568,2282,1127],{"className":2283},[903],[568,2285],{"className":2286,"style":2287},[660],"margin-right:1em;",[568,2289],{"className":2290,"style":899},[660],[568,2292,917],{"className":2293},[656],[568,2295,2296,2299],{"style":2124},[568,2297],{"className":2298,"style":700},[699],[568,2300,2302,2305,2308,2311,2314,2317,2320,2326],{"className":2301},[656],[568,2303],{"className":2304},[656],[568,2306],{"className":2307,"style":899},[660],[568,2309,1127],{"className":2310},[903],[568,2312],{"className":2313,"style":2287},[660],[568,2315],{"className":2316,"style":899},[660],[568,2318,917],{"className":2319},[656],[568,2321,2323],{"className":2322},[656],[568,2324,925],{"className":2325},[924],[568,2327,2329],{"className":2328},[656],"25",[568,2331,2332,2335],{"style":2148},[568,2333],{"className":2334,"style":700},[699],[568,2336,2338,2341,2344,2347,2350,2353,2356,2359,2365],{"className":2337},[656],[568,2339],{"className":2340},[656],[568,2342],{"className":2343,"style":899},[660],[568,2345,1127],{"className":2346},[903],[568,2348],{"className":2349,"style":2287},[660],[568,2351,876],{"className":2352},[903],[568,2354],{"className":2355,"style":899},[660],[568,2357,917],{"className":2358},[656],[568,2360,2362],{"className":2361},[656],[568,2363,925],{"className":2364},[924],[568,2366,2368],{"className":2367},[656],"5937",[568,2370,2371,2374],{"style":2172},[568,2372],{"className":2373,"style":700},[699],[568,2375,2377,2380,2383,2386,2389,2392,2395,2398,2404],{"className":2376},[656],[568,2378],{"className":2379},[656],[568,2381],{"className":2382,"style":899},[660],[568,2384,1127],{"className":2385},[903],[568,2387],{"className":2388,"style":2287},[660],[568,2390,876],{"className":2391},[903],[568,2393],{"className":2394,"style":899},[660],[568,2396,917],{"className":2397},[656],[568,2399,2401],{"className":2400},[656],[568,2402,925],{"className":2403},[924],[568,2405,2407],{"className":2406},[656],"6130",[568,2409,2410,2413],{"style":2196},[568,2411],{"className":2412,"style":700},[699],[568,2414,2416,2419,2422,2425,2428,2431,2434,2437,2443],{"className":2415},[656],[568,2417],{"className":2418},[656],[568,2420],{"className":2421,"style":899},[660],[568,2423,1127],{"className":2424},[903],[568,2426],{"className":2427,"style":2287},[660],[568,2429,876],{"className":2430},[903],[568,2432],{"className":2433,"style":899},[660],[568,2435,917],{"className":2436},[656],[568,2438,2440],{"className":2439},[656],[568,2441,925],{"className":2442},[924],[568,2444,2446],{"className":2445},[656],"7048",[568,2448,2449,2452],{"style":2220},[568,2450],{"className":2451,"style":700},[699],[568,2453,2455,2458,2461,2464,2467,2470,2473,2476,2482],{"className":2454},[656],[568,2456],{"className":2457},[656],[568,2459],{"className":2460,"style":899},[660],[568,2462,1127],{"className":2463},[903],[568,2465],{"className":2466,"style":2287},[660],[568,2468,876],{"className":2469},[903],[568,2471],{"className":2472,"style":899},[660],[568,2474,917],{"className":2475},[656],[568,2477,2479],{"className":2478},[656],[568,2480,925],{"className":2481},[924],[568,2483,2485],{"className":2484},[656],"7169",[568,2487,745],{"className":2488},[744],[568,2490,2492],{"className":2491},[687],[568,2493,2495],{"className":2494,"style":2251},[691],[568,2496],{},[564,2498,2499,2500,2551,2552,2580],{},"Selbst bei ",[568,2501,2503,2521],{"className":2502},[571],[568,2504,2506],{"className":2505},[575],[577,2507,2508],{"xmlns":579},[581,2509,2510,2518],{},[584,2511,2512,2514,2516],{},[609,2513,611],{},[592,2515,1153],{},[597,2517,2047],{},[618,2519,2520],{"encoding":620},"n = 1000",[568,2522,2524,2542],{"className":2523,"ariaHidden":594},[625],[568,2525,2527,2530,2533,2536,2539],{"className":2526},[629],[568,2528],{"className":2529,"style":818},[633],[568,2531,611],{"className":2532},[656,714],[568,2534],{"className":2535,"style":899},[660],[568,2537,1153],{"className":2538},[903],[568,2540],{"className":2541,"style":899},[660],[568,2543,2545,2548],{"className":2544},[629],[568,2546],{"className":2547,"style":849},[633],[568,2549,2047],{"className":2550},[656]," stimmen erst zwei Nachkommastellen. Die Exponentialreihe liefert ",[568,2553,2555,2568],{"className":2554},[571],[568,2556,2558],{"className":2557},[575],[577,2559,2560],{"xmlns":579},[581,2561,2562,2566],{},[584,2563,2564],{},[609,2565,873],{},[618,2567,873],{"encoding":620},[568,2569,2571],{"className":2570,"ariaHidden":594},[625],[568,2572,2574,2577],{"className":2573},[629],[568,2575],{"className":2576,"style":818},[633],[568,2578,873],{"className":2579},[656,714]," wesentlich schneller.",[564,2582,2583,2584,2749,2750,2778,2779,2873],{},"Mit der Verallgemeinerung ist ",[568,2585,2587,2619],{"className":2586},[571],[568,2588,2590],{"className":2589},[575],[577,2591,2592],{"xmlns":579},[581,2593,2594,2616],{},[584,2595,2596],{},[587,2597,2598,2614],{},[584,2599,2600,2602,2604,2606,2612],{},[592,2601,595],{"fence":594},[597,2603,599],{},[592,2605,602],{},[604,2607,2608,2610],{},[597,2609,917],{},[609,2611,611],{},[592,2613,614],{"fence":594},[609,2615,611],{},[618,2617,2618],{"encoding":620},"\\left(1 + \\frac{2}{n}\\right)^n",[568,2620,2622],{"className":2621,"ariaHidden":594},[625],[568,2623,2625,2628],{"className":2624},[629],[568,2626],{"className":2627,"style":634},[633],[568,2629,2631,2726],{"className":2630},[638],[568,2632,2634,2640,2643,2646,2649,2652,2720],{"className":2633},[638],[568,2635,2637],{"className":2636,"style":647},[645,646],[568,2638,595],{"className":2639},[651,652],[568,2641,599],{"className":2642},[656],[568,2644],{"className":2645,"style":661},[660],[568,2647,602],{"className":2648},[665],[568,2650],{"className":2651,"style":661},[660],[568,2653,2655,2658,2717],{"className":2654},[656],[568,2656],{"className":2657},[645,675],[568,2659,2661],{"className":2660},[604],[568,2662,2664,2709],{"className":2663},[682,683],[568,2665,2667,2706],{"className":2666},[687],[568,2668,2670,2684,2692],{"className":2669,"style":692},[691],[568,2671,2672,2675],{"style":695},[568,2673],{"className":2674,"style":700},[699],[568,2676,2678],{"className":2677},[704,705,706,707],[568,2679,2681],{"className":2680},[656,707],[568,2682,611],{"className":2683},[656,714,707],[568,2685,2686,2689],{"style":717},[568,2687],{"className":2688,"style":700},[699],[568,2690],{"className":2691,"style":725},[724],[568,2693,2694,2697],{"style":728},[568,2695],{"className":2696,"style":700},[699],[568,2698,2700],{"className":2699},[704,705,706,707],[568,2701,2703],{"className":2702},[656,707],[568,2704,917],{"className":2705},[656,707],[568,2707,745],{"className":2708},[744],[568,2710,2712],{"className":2711},[687],[568,2713,2715],{"className":2714,"style":752},[691],[568,2716],{},[568,2718],{"className":2719},[758,675],[568,2721,2723],{"className":2722,"style":647},[758,646],[568,2724,614],{"className":2725},[651,652],[568,2727,2729],{"className":2728},[768],[568,2730,2732],{"className":2731},[682],[568,2733,2735],{"className":2734},[687],[568,2736,2738],{"className":2737,"style":778},[691],[568,2739,2740,2743],{"style":781},[568,2741],{"className":2742,"style":785},[699],[568,2744,2746],{"className":2745},[704,705,706,707],[568,2747,611],{"className":2748},[656,714,707]," für große ",[568,2751,2753,2766],{"className":2752},[571],[568,2754,2756],{"className":2755},[575],[577,2757,2758],{"xmlns":579},[581,2759,2760,2764],{},[584,2761,2762],{},[609,2763,611],{},[618,2765,611],{"encoding":620},[568,2767,2769],{"className":2768,"ariaHidden":594},[625],[568,2770,2772,2775],{"className":2771},[629],[568,2773],{"className":2774,"style":818},[633],[568,2776,611],{"className":2777},[656,714]," ungefähr ",[568,2780,2782,2805],{"className":2781},[571],[568,2783,2785],{"className":2784},[575],[577,2786,2787],{"xmlns":579},[581,2788,2789,2802],{},[584,2790,2791,2797,2799],{},[587,2792,2793,2795],{},[609,2794,873],{},[597,2796,917],{},[592,2798,876],{},[597,2800,2801],{},"7,389",[618,2803,2804],{"encoding":620},"e^2 \\approx 7{,}389",[568,2806,2808,2853],{"className":2807,"ariaHidden":594},[625],[568,2809,2811,2815,2844,2847,2850],{"className":2810},[629],[568,2812],{"className":2813,"style":2814},[633],"height:0.8141em;",[568,2816,2818,2821],{"className":2817},[656],[568,2819,873],{"className":2820},[656,714],[568,2822,2824],{"className":2823},[768],[568,2825,2827],{"className":2826},[682],[568,2828,2830],{"className":2829},[687],[568,2831,2833],{"className":2832,"style":2814},[691],[568,2834,2835,2838],{"style":1043},[568,2836],{"className":2837,"style":785},[699],[568,2839,2841],{"className":2840},[704,705,706,707],[568,2842,917],{"className":2843},[656,707],[568,2845],{"className":2846,"style":899},[660],[568,2848,876],{"className":2849},[903],[568,2851],{"className":2852,"style":899},[660],[568,2854,2856,2859,2863,2869],{"className":2855},[629],[568,2857],{"className":2858,"style":913},[633],[568,2860,2862],{"className":2861},[656],"7",[568,2864,2866],{"className":2865},[656],[568,2867,925],{"className":2868},[924],[568,2870,2872],{"className":2871},[656],"389",".",[559,2875,2877],{"id":2876},"typische-fehler","Typische Fehler",[2879,2880,2881,3175,3207],"ul",{},[2882,2883,2884,2885,2966,2967,3088,3089,3117,3118,3146,3147,2873],"li",{},"„",[568,2886,2888,2910],{"className":2887},[571],[568,2889,2891],{"className":2890},[575],[577,2892,2893],{"xmlns":579},[581,2894,2895,2907],{},[584,2896,2897,2903,2905],{},[587,2898,2899,2901],{},[597,2900,599],{},[609,2902,1174],{"mathvariant":1173},[592,2904,1153],{},[597,2906,599],{},[618,2908,2909],{"encoding":620},"1^\\infty = 1",[568,2911,2913,2957],{"className":2912,"ariaHidden":594},[625],[568,2914,2916,2919,2948,2951,2954],{"className":2915},[629],[568,2917],{"className":2918,"style":1022},[633],[568,2920,2922,2925],{"className":2921},[656],[568,2923,599],{"className":2924},[656],[568,2926,2928],{"className":2927},[768],[568,2929,2931],{"className":2930},[682],[568,2932,2934],{"className":2933},[687],[568,2935,2937],{"className":2936,"style":1022},[691],[568,2938,2939,2942],{"style":1043},[568,2940],{"className":2941,"style":785},[699],[568,2943,2945],{"className":2944},[704,705,706,707],[568,2946,1174],{"className":2947},[656,707],[568,2949],{"className":2950,"style":899},[660],[568,2952,1153],{"className":2953},[903],[568,2955],{"className":2956,"style":899},[660],[568,2958,2960,2963],{"className":2959},[629],[568,2961],{"className":2962,"style":849},[633],[568,2964,599],{"className":2965},[656],"“ schließen. Die Basis ",[568,2968,2970,2992],{"className":2969},[571],[568,2971,2973],{"className":2972},[575],[577,2974,2975],{"xmlns":579},[581,2976,2977,2989],{},[584,2978,2979,2981,2983],{},[597,2980,599],{},[592,2982,602],{},[604,2984,2985,2987],{},[597,2986,599],{},[609,2988,611],{},[618,2990,2991],{"encoding":620},"1 + \\frac{1}{n}",[568,2993,2995,3014],{"className":2994,"ariaHidden":594},[625],[568,2996,2998,3002,3005,3008,3011],{"className":2997},[629],[568,2999],{"className":3000,"style":3001},[633],"height:0.7278em;vertical-align:-0.0833em;",[568,3003,599],{"className":3004},[656],[568,3006],{"className":3007,"style":661},[660],[568,3009,602],{"className":3010},[665],[568,3012],{"className":3013,"style":661},[660],[568,3015,3017,3020],{"className":3016},[629],[568,3018],{"className":3019,"style":1547},[633],[568,3021,3023,3026,3085],{"className":3022},[656],[568,3024],{"className":3025},[645,675],[568,3027,3029],{"className":3028},[604],[568,3030,3032,3077],{"className":3031},[682,683],[568,3033,3035,3074],{"className":3034},[687],[568,3036,3038,3052,3060],{"className":3037,"style":692},[691],[568,3039,3040,3043],{"style":695},[568,3041],{"className":3042,"style":700},[699],[568,3044,3046],{"className":3045},[704,705,706,707],[568,3047,3049],{"className":3048},[656,707],[568,3050,611],{"className":3051},[656,714,707],[568,3053,3054,3057],{"style":717},[568,3055],{"className":3056,"style":700},[699],[568,3058],{"className":3059,"style":725},[724],[568,3061,3062,3065],{"style":728},[568,3063],{"className":3064,"style":700},[699],[568,3066,3068],{"className":3067},[704,705,706,707],[568,3069,3071],{"className":3070},[656,707],[568,3072,599],{"className":3073},[656,707],[568,3075,745],{"className":3076},[744],[568,3078,3080],{"className":3079},[687],[568,3081,3083],{"className":3082,"style":752},[691],[568,3084],{},[568,3086],{"className":3087},[758,675]," ist immer etwas größer als ",[568,3090,3092,3105],{"className":3091},[571],[568,3093,3095],{"className":3094},[575],[577,3096,3097],{"xmlns":579},[581,3098,3099,3103],{},[584,3100,3101],{},[597,3102,599],{},[618,3104,599],{"encoding":620},[568,3106,3108],{"className":3107,"ariaHidden":594},[625],[568,3109,3111,3114],{"className":3110},[629],[568,3112],{"className":3113,"style":849},[633],[568,3115,599],{"className":3116},[656],", und der Exponent wächst gleichzeitig. Der Grenzwert ist ",[568,3119,3121,3134],{"className":3120},[571],[568,3122,3124],{"className":3123},[575],[577,3125,3126],{"xmlns":579},[581,3127,3128,3132],{},[584,3129,3130],{},[609,3131,873],{},[618,3133,873],{"encoding":620},[568,3135,3137],{"className":3136,"ariaHidden":594},[625],[568,3138,3140,3143],{"className":3139},[629],[568,3141],{"className":3142,"style":818},[633],[568,3144,873],{"className":3145},[656,714],", nicht ",[568,3148,3150,3163],{"className":3149},[571],[568,3151,3153],{"className":3152},[575],[577,3154,3155],{"xmlns":579},[581,3156,3157,3161],{},[584,3158,3159],{},[597,3160,599],{},[618,3162,599],{"encoding":620},[568,3164,3166],{"className":3165,"ariaHidden":594},[625],[568,3167,3169,3172],{"className":3168},[629],[568,3170],{"className":3171,"style":849},[633],[568,3173,599],{"className":3174},[656],[2882,3176,3177,3178,3206],{},"Glauben, die Folge wachse unbegrenzt. Sie ist nach oben durch ",[568,3179,3181,3194],{"className":3180},[571],[568,3182,3184],{"className":3183},[575],[577,3185,3186],{"xmlns":579},[581,3187,3188,3192],{},[584,3189,3190],{},[597,3191,837],{},[618,3193,837],{"encoding":620},[568,3195,3197],{"className":3196,"ariaHidden":594},[625],[568,3198,3200,3203],{"className":3199},[629],[568,3201],{"className":3202,"style":849},[633],[568,3204,837],{"className":3205},[656]," beschränkt.",[2882,3208,3209,3237,3238,3277],{},[568,3210,3212,3225],{"className":3211},[571],[568,3213,3215],{"className":3214},[575],[577,3216,3217],{"xmlns":579},[581,3218,3219,3223],{},[584,3220,3221],{},[609,3222,873],{},[618,3224,873],{"encoding":620},[568,3226,3228],{"className":3227,"ariaHidden":594},[625],[568,3229,3231,3234],{"className":3230},[629],[568,3232],{"className":3233,"style":818},[633],[568,3235,873],{"className":3236},[656,714]," mit dem gerundeten Wert ",[568,3239,3241,3256],{"className":3240},[571],[568,3242,3244],{"className":3243},[575],[577,3245,3246],{"xmlns":579},[581,3247,3248,3253],{},[584,3249,3250],{},[597,3251,3252],{},"2,7",[618,3254,3255],{"encoding":620},"2{,}7",[568,3257,3259],{"className":3258,"ariaHidden":594},[625],[568,3260,3262,3265,3268,3274],{"className":3261},[629],[568,3263],{"className":3264,"style":913},[633],[568,3266,917],{"className":3267},[656],[568,3269,3271],{"className":3270},[656],[568,3272,925],{"className":3273},[924],[568,3275,2862],{"className":3276},[656]," gleichsetzen und dann mit vielen Stellen weiterrechnen.",{"title":3279,"searchDepth":3280,"depth":3280,"links":3281},"",2,[3282,3283,3284],{"id":561,"depth":3280,"text":562},{"id":1823,"depth":3280,"text":1824},{"id":2876,"depth":3280,"text":2877},[3286,3288,3291,3294,3297,3300,3303,3306,3309,3311],{"lhs":3287,"rhs":917},"(1 + 1\u002F1)^1",{"lhs":3289,"rhs":3290},"(1 + 1\u002F2)^2","2.25",{"lhs":3292,"rhs":3293},"round((1 + 1\u002F10)^10, 4)","2.5937",{"lhs":3295,"rhs":3296},"round((1 + 1\u002F12)^12, 4)","2.613",{"lhs":3298,"rhs":3299},"round((1 + 1\u002F100)^100, 4)","2.7048",{"lhs":3301,"rhs":3302},"round((1 + 1\u002F1000)^1000, 4)","2.7169",{"lhs":3304,"rhs":3305},"round(exp(1), 5)","2.71828",{"lhs":3307,"rhs":3308},"round((1 + 2\u002F10^7)^(10^7), 3)","round(exp(2), 3)",{"lhs":3308,"rhs":3310},"7.389",{"lhs":3312,"rhs":3305},"round((1 + 1\u002F10^6)^(10^6), 5)",null,"md","euler-number-limit","e = \\lim_{n \\to \\infty} \\left( 1 + \\frac{1}{n} \\right)^n \\approx 2{,}71828","\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>e\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\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>\u003Cmsup>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>+\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>≈\u003C\u002Fmo>\u003Cmn>2,71828\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">e = \\lim_{n \\to \\infty} \\left( 1 + \\frac{1}{n} \\right)^n \\approx 2{,}71828\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">e\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:2.4543em;vertical-align:-0.95em;\">\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=\"minner\">\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.5043em;\">\u003Cspan style=\"top:-3.9029em;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>\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:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">71828\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fsequences-series\u002Feulersche-zahl-grenzwert",[],[3324,3325,3326,3327],"exponential-function","exponential-series","compound-interest","exponential-growth",{"title":548,"description":3279},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Feulersche-zahl-grenzwert","Die Eulersche Zahl e ≈ 2,71828 ist der Grenzwert der Folge (1 + 1\u002Fn)ⁿ für n gegen unendlich.",[3332,3333,3334,3335],"eulersche zahl","grenzwert","folge","exponentialfunktion",[3337,3340],{"symbol":873,"meaning":3338,"symbolHtml":3339},"Eulersche Zahl, Basis der natürlichen Exponentialfunktion","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>e\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">e\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">e\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":611,"meaning":3341,"symbolHtml":3342},"natürliche Zahl, die gegen unendlich geht","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","wZrkeDzHbAbSw0L79sL8_gfC2LkH7jbmugRJbxOlj0E",[3345,3348,3351,3354],{"stem":3346,"title":3347,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fexponentialfunktion","Exponentialfunktion",{"stem":3349,"title":3350,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fexponentielles-wachstum","Exponentielles Wachstum",{"stem":3352,"title":3353,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fzinseszins","Zinseszins",{"stem":3355,"title":3356,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fexponentialreihe","Exponentialreihe",1793824263879]