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72,1182],{},[572,1184],{"className":1185},[946,881],[572,1187],{"className":1188,"style":1089},[1019],[572,1190,799],{"className":1191},[1093],[572,1193],{"className":1194,"style":1089},[1019],[572,1196,1198,1202],{"className":1197},[613],[572,1199],{"className":1200,"style":1201},[617],"height:0.6444em;",[572,1203,802],{"className":1204},[622],[564,1206,1207,1208,1211,1212,1492,1493,1627,1628,1723,1724,1794,1795,1893],{},"In der Analysis dient die Reihe oft als ",[568,1209,1210],{},"Definition"," der Exponentialfunktion: ",[572,1213,1215,1275],{"className":1214},[575],[572,1216,1218],{"className":1217},[579],[581,1219,1220],{"xmlns":583},[585,1221,1222,1272],{},[588,1223,1224,1227,1230,1232,1234,1236,1239,1241,1258],{},[594,1225,1226],{},"exp",[716,1228,1229],{},"⁡",[716,1231,747],{"stretchy":746},[594,1233,599],{},[716,1235,756],{"stretchy":746},[716,1237,1238],{},":",[716,1240,778],{},[1242,1243,1244,1247,1255],"msubsup",{},[716,1245,1246],{},"∑",[588,1248,1249,1251,1253],{},[594,1250,732],{},[716,1252,778],{},[737,1254,802],{},[594,1256,1257],{"mathvariant":742},"∞",[720,1259,1260,1266],{},[591,1261,1262,1264],{},[594,1263,599],{},[594,1265,732],{},[588,1267,1268,1270],{},[594,1269,732],{},[716,1271,759],{"stretchy":746},[601,1273,1274],{"encoding":603},"\\exp(x) := \\sum_{k=0}^\\infty \\frac{x^k}{k!}",[572,1276,1278,1308],{"className":1277,"ariaHidden":609},[608],[572,1279,1281,1285,1289,1292,1295,1298,1301,1305],{"className":1280},[613],[572,1282],{"className":1283,"style":1284},[617],"height:1em;vertical-align:-0.25em;",[572,1286,1226],{"className":1287},[1288],"mop",[572,1290,747],{"className":1291},[823],[572,1293,599],{"className":1294},[622,626],[572,1296,756],{"className":1297},[946],[572,1299],{"className":1300,"style":1089},[1019],[572,1302,1304],{"className":1303},[1093],":=",[572,1306],{"className":1307,"style":1089},[1019],[572,1309,1311,1315,1382,1386],{"className":1310},[613],[572,1312],{"className":1313,"style":1314},[617],"height:1.3879em;vertical-align:-0.345em;",[572,1316,1318,1324],{"className":1317},[1288],[572,1319,1246],{"className":1320,"style":1323},[1288,1321,1322],"op-symbol","small-op","position:relative;top:0em;",[572,1325,1327],{"className":1326},[630],[572,1328,1330,1373],{"className":1329},[634,832],[572,1331,1333,1370],{"className":1332},[638],[572,1334,1337,1358],{"className":1335,"style":1336},[642],"height:0.8043em;",[572,1338,1340,1343],{"style":1339},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[572,1341],{"className":1342,"style":650},[649],[572,1344,1346],{"className":1345},[654,655,656,657],[572,1347,1349,1352,1355],{"className":1348},[622,657],[572,1350,732],{"className":1351,"style":936},[622,626,657],[572,1353,778],{"className":1354},[1093,657],[572,1356,802],{"className":1357},[622,657],[572,1359,1361,1364],{"style":1360},"top:-3.2029em;margin-right:0.05em;",[572,1362],{"className":1363,"style":650},[649],[572,1365,1367],{"className":1366},[654,655,656,657],[572,1368,1257],{"className":1369},[622,657],[572,1371,865],{"className":1372},[864],[572,1374,1376],{"className":1375},[638],[572,1377,1380],{"className":1378,"style":1379},[642],"height:0.2997em;",[572,1381],{},[572,1383],{"className":1384,"style":1385},[1019],"margin-right:0.1667em;",[572,1387,1389,1392,1489],{"className":1388},[622],[572,1390],{"className":1391},[823,881],[572,1393,1395],{"className":1394},[720],[572,1396,1398,1480],{"className":1397},[634,832],[572,1399,1401,1477],{"className":1400},[638],[572,1402,1405,1423,1431],{"className":1403,"style":1404},[642],"height:1.0429em;",[572,1406,1408,1411],{"style":1407},"top:-2.655em;",[572,1409],{"className":1410,"style":901},[649],[572,1412,1414],{"className":1413},[654,655,656,657],[572,1415,1417,1420],{"className":1416},[622,657],[572,1418,732],{"className":1419,"style":936},[622,626,657],[572,1421,759],{"className":1422},[946,657],[572,1424,1425,1428],{"style":949},[572,1426],{"className":1427,"style":901},[649],[572,1429],{"className":1430,"style":957},[956],[572,1432,1434,1437],{"style":1433},"top:-3.394em;",[572,1435],{"className":1436,"style":901},[649],[572,1438,1440],{"className":1439},[654,655,656,657],[572,1441,1443],{"className":1442},[622,657],[572,1444,1446,1449],{"className":1445},[622,657],[572,1447,599],{"className":1448},[622,626,657],[572,1450,1452],{"className":1451},[630],[572,1453,1455],{"className":1454},[634],[572,1456,1458],{"className":1457},[638],[572,1459,1462],{"className":1460,"style":1461},[642],"height:0.927em;",[572,1463,1465,1469],{"style":1464},"top:-2.931em;margin-right:0.0714em;",[572,1466],{"className":1467,"style":1468},[649],"height:2.5em;",[572,1470,1474],{"className":1471},[654,1472,1473,657],"reset-size3","size1",[572,1475,732],{"className":1476,"style":936},[622,626,657],[572,1478,865],{"className":1479},[864],[572,1481,1483],{"className":1482},[638],[572,1484,1487],{"className":1485,"style":1486},[642],"height:0.345em;",[572,1488],{},[572,1490],{"className":1491},[946,881],". Daraus folgen die Funktionalgleichung ",[572,1494,1496,1545],{"className":1495},[575],[572,1497,1499],{"className":1498},[579],[581,1500,1501],{"xmlns":583},[585,1502,1503,1542],{},[588,1504,1505,1507,1509,1511,1513,1515,1518,1520,1522,1524,1526,1528,1530,1532,1534,1536,1538,1540],{},[594,1506,1226],{},[716,1508,1229],{},[716,1510,747],{"stretchy":746},[594,1512,599],{},[716,1514,735],{},[594,1516,1517],{},"y",[716,1519,756],{"stretchy":746},[716,1521,778],{},[594,1523,1226],{},[716,1525,1229],{},[716,1527,747],{"stretchy":746},[594,1529,599],{},[716,1531,756],{"stretchy":746},[594,1533,1226],{},[716,1535,1229],{},[716,1537,747],{"stretchy":746},[594,1539,1517],{},[716,1541,756],{"stretchy":746},[601,1543,1544],{"encoding":603},"\\exp(x + y) = \\exp(x) \\exp(y)",[572,1546,1548,1572,1594],{"className":1547,"ariaHidden":609},[608],[572,1549,1551,1554,1557,1560,1563,1566,1569],{"className":1550},[613],[572,1552],{"className":1553,"style":1284},[617],[572,1555,1226],{"className":1556},[1288],[572,1558,747],{"className":1559},[823],[572,1561,599],{"className":1562},[622,626],[572,1564],{"className":1565,"style":1020},[1019],[572,1567,735],{"className":1568},[1003],[572,1570],{"className":1571,"style":1020},[1019],[572,1573,1575,1578,1582,1585,1588,1591],{"className":1574},[613],[572,1576],{"className":1577,"style":1284},[617],[572,1579,1517],{"className":1580,"style":1581},[622,626],"margin-right:0.0359em;",[572,1583,756],{"className":1584},[946],[572,1586],{"className":1587,"style":1089},[1019],[572,1589,778],{"className":1590},[1093],[572,1592],{"className":1593,"style":1089},[1019],[572,1595,1597,1600,1603,1606,1609,1612,1615,1618,1621,1624],{"className":1596},[613],[572,1598],{"className":1599,"style":1284},[617],[572,1601,1226],{"className":1602},[1288],[572,1604,747],{"className":1605},[823],[572,1607,599],{"className":1608},[622,626],[572,1610,756],{"className":1611},[946],[572,1613],{"className":1614,"style":1385},[1019],[572,1616,1226],{"className":1617},[1288],[572,1619,747],{"className":1620},[823],[572,1622,1517],{"className":1623,"style":1581},[622,626],[572,1625,756],{"className":1626},[946]," (über das Cauchy-Produkt) und ",[572,1629,1631,1661],{"className":1630},[575],[572,1632,1634],{"className":1633},[579],[581,1635,1636],{"xmlns":583},[585,1637,1638,1658],{},[588,1639,1640,1652,1654,1656],{},[591,1641,1642,1648],{},[588,1643,1644,1646],{},[594,1645,1226],{},[716,1647,1229],{},[716,1649,1651],{"mathvariant":742,"lspace":1650,"rspace":1650},"0em","′",[716,1653,778],{},[594,1655,1226],{},[716,1657,1229],{},[601,1659,1660],{"encoding":603},"\\exp' = \\exp",[572,1662,1664,1713],{"className":1663,"ariaHidden":609},[608],[572,1665,1667,1671,1704,1707,1710],{"className":1666},[613],[572,1668],{"className":1669,"style":1670},[617],"height:0.9463em;vertical-align:-0.1944em;",[572,1672,1674,1677],{"className":1673},[1288],[572,1675,1226],{"className":1676},[1288],[572,1678,1680],{"className":1679},[630],[572,1681,1683],{"className":1682},[634],[572,1684,1686],{"className":1685},[638],[572,1687,1690],{"className":1688,"style":1689},[642],"height:0.7519em;",[572,1691,1692,1695],{"style":645},[572,1693],{"className":1694,"style":650},[649],[572,1696,1698],{"className":1697},[654,655,656,657],[572,1699,1701],{"className":1700},[622,657],[572,1702,1651],{"className":1703},[622,657],[572,1705],{"className":1706,"style":1089},[1019],[572,1708,778],{"className":1709},[1093],[572,1711],{"className":1712,"style":1089},[1019],[572,1714,1716,1720],{"className":1715},[613],[572,1717],{"className":1718,"style":1719},[617],"height:0.625em;vertical-align:-0.1944em;",[572,1721,1226],{"className":1722},[1288]," (gliedweises Ableiten einer Potenzreihe). Mit ",[572,1725,1727,1755],{"className":1726},[575],[572,1728,1730],{"className":1729},[579],[581,1731,1732],{"xmlns":583},[585,1733,1734,1752],{},[588,1735,1736,1738,1740,1742,1744,1746,1748,1750],{},[594,1737,596],{},[716,1739,1238],{},[716,1741,778],{},[594,1743,1226],{},[716,1745,1229],{},[716,1747,747],{"stretchy":746},[737,1749,739],{},[716,1751,756],{"stretchy":746},[601,1753,1754],{"encoding":603},"e := \\exp(1)",[572,1756,1758,1776],{"className":1757,"ariaHidden":609},[608],[572,1759,1761,1764,1767,1770,1773],{"className":1760},[613],[572,1762],{"className":1763,"style":691},[617],[572,1765,596],{"className":1766},[622,626],[572,1768],{"className":1769,"style":1089},[1019],[572,1771,1304],{"className":1772},[1093],[572,1774],{"className":1775,"style":1089},[1019],[572,1777,1779,1782,1785,1788,1791],{"className":1778},[613],[572,1780],{"className":1781,"style":1284},[617],[572,1783,1226],{"className":1784},[1288],[572,1786,747],{"className":1787},[823],[572,1789,739],{"className":1790},[622],[572,1792,756],{"className":1793},[946]," gilt dann ",[572,1796,1798,1828],{"className":1797},[575],[572,1799,1801],{"className":1800},[579],[581,1802,1803],{"xmlns":583},[585,1804,1805,1825],{},[588,1806,1807,1809,1811,1813,1815,1817,1819],{},[594,1808,1226],{},[716,1810,1229],{},[716,1812,747],{"stretchy":746},[594,1814,599],{},[716,1816,756],{"stretchy":746},[716,1818,778],{},[591,1820,1821,1823],{},[594,1822,596],{},[594,1824,599],{},[601,1826,1827],{"encoding":603},"\\exp(x) = e^x",[572,1829,1831,1858],{"className":1830,"ariaHidden":609},[608],[572,1832,1834,1837,1840,1843,1846,1849,1852,1855],{"className":1833},[613],[572,1835],{"className":1836,"style":1284},[617],[572,1838,1226],{"className":1839},[1288],[572,1841,747],{"className":1842},[823],[572,1844,599],{"className":1845},[622,626],[572,1847,756],{"className":1848},[946],[572,1850],{"className":1851,"style":1089},[1019],[572,1853,778],{"className":1854},[1093],[572,1856],{"className":1857,"style":1089},[1019],[572,1859,1861,1864],{"className":1860},[613],[572,1862],{"className":1863,"style":618},[617],[572,1865,1867,1870],{"className":1866},[622],[572,1868,596],{"className":1869},[622,626],[572,1871,1873],{"className":1872},[630],[572,1874,1876],{"className":1875},[634],[572,1877,1879],{"className":1878},[638],[572,1880,1882],{"className":1881,"style":618},[642],[572,1883,1884,1887],{"style":645},[572,1885],{"className":1886,"style":650},[649],[572,1888,1890],{"className":1889},[654,655,656,657],[572,1891,599],{"className":1892},[622,626,657],".",[564,1895,1896,1897,1955,1956,2053,2054,2112,2113,2141,2142,2170,2171,1893],{},"Die Reihe ist zugleich die Taylorreihe von ",[572,1898,1900,1917],{"className":1899},[575],[572,1901,1903],{"className":1902},[579],[581,1904,1905],{"xmlns":583},[585,1906,1907,1915],{},[588,1908,1909],{},[591,1910,1911,1913],{},[594,1912,596],{},[594,1914,599],{},[601,1916,604],{"encoding":603},[572,1918,1920],{"className":1919,"ariaHidden":609},[608],[572,1921,1923,1926],{"className":1922},[613],[572,1924],{"className":1925,"style":618},[617],[572,1927,1929,1932],{"className":1928},[622],[572,1930,596],{"className":1931},[622,626],[572,1933,1935],{"className":1934},[630],[572,1936,1938],{"className":1937},[634],[572,1939,1941],{"className":1940},[638],[572,1942,1944],{"className":1943,"style":618},[642],[572,1945,1946,1949],{"style":645},[572,1947],{"className":1948,"style":650},[649],[572,1950,1952],{"className":1951},[654,655,656,657],[572,1953,599],{"className":1954},[622,626,657]," um ",[572,1957,1959,1982],{"className":1958},[575],[572,1960,1962],{"className":1961},[579],[581,1963,1964],{"xmlns":583},[585,1965,1966,1979],{},[588,1967,1968,1975,1977],{},[1969,1970,1971,1973],"msub",{},[594,1972,599],{},[737,1974,802],{},[716,1976,778],{},[737,1978,802],{},[601,1980,1981],{"encoding":603},"x_0 = 0",[572,1983,1985,2044],{"className":1984,"ariaHidden":609},[608],[572,1986,1988,1992,2035,2038,2041],{"className":1987},[613],[572,1989],{"className":1990,"style":1991},[617],"height:0.5806em;vertical-align:-0.15em;",[572,1993,1995,1998],{"className":1994},[622],[572,1996,599],{"className":1997},[622,626],[572,1999,2001],{"className":2000},[630],[572,2002,2004,2026],{"className":2003},[634,832],[572,2005,2007,2023],{"className":2006},[638],[572,2008,2011],{"className":2009,"style":2010},[642],"height:0.3011em;",[572,2012,2014,2017],{"style":2013},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[572,2015],{"className":2016,"style":650},[649],[572,2018,2020],{"className":2019},[654,655,656,657],[572,2021,802],{"className":2022},[622,657],[572,2024,865],{"className":2025},[864],[572,2027,2029],{"className":2028},[638],[572,2030,2033],{"className":2031,"style":2032},[642],"height:0.15em;",[572,2034],{},[572,2036],{"className":2037,"style":1089},[1019],[572,2039,778],{"className":2040},[1093],[572,2042],{"className":2043,"style":1089},[1019],[572,2045,2047,2050],{"className":2046},[613],[572,2048],{"className":2049,"style":1201},[617],[572,2051,802],{"className":2052},[622],", denn alle Ableitungen von ",[572,2055,2057,2074],{"className":2056},[575],[572,2058,2060],{"className":2059},[579],[581,2061,2062],{"xmlns":583},[585,2063,2064,2072],{},[588,2065,2066],{},[591,2067,2068,2070],{},[594,2069,596],{},[594,2071,599],{},[601,2073,604],{"encoding":603},[572,2075,2077],{"className":2076,"ariaHidden":609},[608],[572,2078,2080,2083],{"className":2079},[613],[572,2081],{"className":2082,"style":618},[617],[572,2084,2086,2089],{"className":2085},[622],[572,2087,596],{"className":2088},[622,626],[572,2090,2092],{"className":2091},[630],[572,2093,2095],{"className":2094},[634],[572,2096,2098],{"className":2097},[638],[572,2099,2101],{"className":2100,"style":618},[642],[572,2102,2103,2106],{"style":645},[572,2104],{"className":2105,"style":650},[649],[572,2107,2109],{"className":2108},[654,655,656,657],[572,2110,599],{"className":2111},[622,626,657]," haben an der Stelle ",[572,2114,2116,2129],{"className":2115},[575],[572,2117,2119],{"className":2118},[579],[581,2120,2121],{"xmlns":583},[585,2122,2123,2127],{},[588,2124,2125],{},[737,2126,802],{},[601,2128,802],{"encoding":603},[572,2130,2132],{"className":2131,"ariaHidden":609},[608],[572,2133,2135,2138],{"className":2134},[613],[572,2136],{"className":2137,"style":1201},[617],[572,2139,802],{"className":2140},[622]," den Wert ",[572,2143,2145,2158],{"className":2144},[575],[572,2146,2148],{"className":2147},[579],[581,2149,2150],{"xmlns":583},[585,2151,2152,2156],{},[588,2153,2154],{},[737,2155,739],{},[601,2157,739],{"encoding":603},[572,2159,2161],{"className":2160,"ariaHidden":609},[608],[572,2162,2164,2167],{"className":2163},[613],[572,2165],{"className":2166,"style":1201},[617],[572,2168,739],{"className":2169},[622],". Für komplexe Argumente liefert sie die Eulersche Formel ",[572,2172,2174,2218],{"className":2173},[575],[572,2175,2177],{"className":2176},[579],[581,2178,2179],{"xmlns":583},[585,2180,2181,2215],{},[588,2182,2183,2195,2197,2200,2202,2204,2206,2208,2211,2213],{},[591,2184,2185,2187],{},[594,2186,596],{},[588,2188,2189,2192],{},[594,2190,2191],{},"i",[594,2193,2194],{},"φ",[716,2196,778],{},[594,2198,2199],{},"cos",[716,2201,1229],{},[594,2203,2194],{},[716,2205,735],{},[594,2207,2191],{},[594,2209,2210],{},"sin",[716,2212,1229],{},[594,2214,2194],{},[601,2216,2217],{"encoding":603},"e^{i\\varphi} = \\cos \\varphi + i \\sin \\varphi",[572,2219,2221,2272,2297],{"className":2220,"ariaHidden":609},[608],[572,2222,2224,2228,2263,2266,2269],{"className":2223},[613],[572,2225],{"className":2226,"style":2227},[617],"height:0.8247em;",[572,2229,2231,2234],{"className":2230},[622],[572,2232,596],{"className":2233},[622,626],[572,2235,2237],{"className":2236},[630],[572,2238,2240],{"className":2239},[634],[572,2241,2243],{"className":2242},[638],[572,2244,2246],{"className":2245,"style":2227},[642],[572,2247,2248,2251],{"style":645},[572,2249],{"className":2250,"style":650},[649],[572,2252,2254],{"className":2253},[654,655,656,657],[572,2255,2257,2260],{"className":2256},[622,657],[572,2258,2191],{"className":2259},[622,626,657],[572,2261,2194],{"className":2262},[622,626,657],[572,2264],{"className":2265,"style":1089},[1019],[572,2267,778],{"className":2268},[1093],[572,2270],{"className":2271,"style":1089},[1019],[572,2273,2275,2279,2282,2285,2288,2291,2294],{"className":2274},[613],[572,2276],{"className":2277,"style":2278},[617],"height:0.7778em;vertical-align:-0.1944em;",[572,2280,2199],{"className":2281},[1288],[572,2283],{"className":2284,"style":1385},[1019],[572,2286,2194],{"className":2287},[622,626],[572,2289],{"className":2290,"style":1020},[1019],[572,2292,735],{"className":2293},[1003],[572,2295],{"className":2296,"style":1020},[1019],[572,2298,2300,2304,2307,2310,2313,2316],{"className":2299},[613],[572,2301],{"className":2302,"style":2303},[617],"height:0.8623em;vertical-align:-0.1944em;",[572,2305,2191],{"className":2306},[622,626],[572,2308],{"className":2309,"style":1385},[1019],[572,2311,2210],{"className":2312},[1288],[572,2314],{"className":2315,"style":1385},[1019],[572,2317,2194],{"className":2318},[622,626],[559,2320,2322],{"id":2321},"beispiele","Beispiele",[564,2324,2325,2326,2377,2378,2406,2407,2460],{},"Für ",[572,2327,2329,2347],{"className":2328},[575],[572,2330,2332],{"className":2331},[579],[581,2333,2334],{"xmlns":583},[585,2335,2336,2344],{},[588,2337,2338,2340,2342],{},[594,2339,599],{},[716,2341,778],{},[737,2343,739],{},[601,2345,2346],{"encoding":603},"x = 1",[572,2348,2350,2368],{"className":2349,"ariaHidden":609},[608],[572,2351,2353,2356,2359,2362,2365],{"className":2352},[613],[572,2354],{"className":2355,"style":691},[617],[572,2357,599],{"className":2358},[622,626],[572,2360],{"className":2361,"style":1089},[1019],[572,2363,778],{"className":2364},[1093],[572,2366],{"className":2367,"style":1089},[1019],[572,2369,2371,2374],{"className":2370},[613],[572,2372],{"className":2373,"style":1201},[617],[572,2375,739],{"className":2376},[622]," ergibt sich ",[572,2379,2381,2394],{"className":2380},[575],[572,2382,2384],{"className":2383},[579],[581,2385,2386],{"xmlns":583},[585,2387,2388,2392],{},[588,2389,2390],{},[594,2391,596],{},[601,2393,596],{"encoding":603},[572,2395,2397],{"className":2396,"ariaHidden":609},[608],[572,2398,2400,2403],{"className":2399},[613],[572,2401],{"className":2402,"style":691},[617],[572,2404,596],{"className":2405},[622,626],". Schon die Glieder bis ",[572,2408,2410,2429],{"className":2409},[575],[572,2411,2413],{"className":2412},[579],[581,2414,2415],{"xmlns":583},[585,2416,2417,2426],{},[588,2418,2419,2421,2423],{},[594,2420,732],{},[716,2422,778],{},[737,2424,2425],{},"6",[601,2427,2428],{"encoding":603},"k = 6",[572,2430,2432,2451],{"className":2431,"ariaHidden":609},[608],[572,2433,2435,2439,2442,2445,2448],{"className":2434},[613],[572,2436],{"className":2437,"style":2438},[617],"height:0.6944em;",[572,2440,732],{"className":2441,"style":936},[622,626],[572,2443],{"className":2444,"style":1089},[1019],[572,2446,778],{"className":2447},[1093],[572,2449],{"className":2450,"style":1089},[1019],[572,2452,2454,2457],{"className":2453},[613],[572,2455],{"className":2456,"style":1201},[617],[572,2458,2425],{"className":2459},[622]," liefern drei richtige Nachkommastellen:",[572,2462,2464],{"className":2463},[699],[572,2465,2467,2539],{"className":2466},[575],[572,2468,2470],{"className":2469},[579],[581,2471,2472],{"xmlns":583,"display":708},[585,2473,2474,2536],{},[588,2475,2476,2478,2481,2483,2485,2487,2489,2496,2498,2504,2506,2513,2515,2522,2524,2531,2533],{},[594,2477,596],{},[716,2479,2480],{},"≈",[737,2482,739],{},[716,2484,735],{},[737,2486,739],{},[716,2488,735],{},[720,2490,2491,2493],{},[737,2492,739],{},[737,2494,2495],{},"2",[716,2497,735],{},[720,2499,2500,2502],{},[737,2501,739],{},[737,2503,2425],{},[716,2505,735],{},[720,2507,2508,2510],{},[737,2509,739],{},[737,2511,2512],{},"24",[716,2514,735],{},[720,2516,2517,2519],{},[737,2518,739],{},[737,2520,2521],{},"120",[716,2523,735],{},[720,2525,2526,2528],{},[737,2527,739],{},[737,2529,2530],{},"720",[716,2532,2480],{},[737,2534,2535],{},"2,7181",[601,2537,2538],{"encoding":603},"e \\approx 1 + 1 + \\frac{1}{2} + \\frac{1}{6} + \\frac{1}{24} + \\frac{1}{120} + \\frac{1}{720} \\approx 2{,}7181",[572,2540,2542,2561,2580,2598,2678,2755,2832,2909,2986],{"className":2541,"ariaHidden":609},[608],[572,2543,2545,2549,2552,2555,2558],{"className":2544},[613],[572,2546],{"className":2547,"style":2548},[617],"height:0.4831em;",[572,2550,596],{"className":2551},[622,626],[572,2553],{"className":2554,"style":1089},[1019],[572,2556,2480],{"className":2557},[1093],[572,2559],{"className":2560,"style":1089},[1019],[572,2562,2564,2568,2571,2574,2577],{"className":2563},[613],[572,2565],{"className":2566,"style":2567},[617],"height:0.7278em;vertical-align:-0.0833em;",[572,2569,739],{"className":2570},[622],[572,2572],{"className":2573,"style":1020},[1019],[572,2575,735],{"className":2576},[1003],[572,2578],{"className":2579,"style":1020},[1019],[572,2581,2583,2586,2589,2592,2595],{"className":2582},[613],[572,2584],{"className":2585,"style":2567},[617],[572,2587,739],{"className":2588},[622],[572,2590],{"className":2591,"style":1020},[1019],[572,2593,735],{"className":2594},[1003],[572,2596],{"className":2597,"style":1020},[1019],[572,2599,2601,2605,2669,2672,2675],{"className":2600},[613],[572,2602],{"className":2603,"style":2604},[617],"height:2.0074em;vertical-align:-0.686em;",[572,2606,2608,2611,2666],{"className":2607},[622],[572,2609],{"className":2610},[823,881],[572,2612,2614],{"className":2613},[720],[572,2615,2617,2657],{"className":2616},[634,832],[572,2618,2620,2654],{"className":2619},[638],[572,2621,2624,2635,2643],{"className":2622,"style":2623},[642],"height:1.3214em;",[572,2625,2626,2629],{"style":897},[572,2627],{"className":2628,"style":901},[649],[572,2630,2632],{"className":2631},[622],[572,2633,2495],{"className":2634},[622],[572,2636,2637,2640],{"style":949},[572,2638],{"className":2639,"style":901},[649],[572,2641],{"className":2642,"style":957},[956],[572,2644,2645,2648],{"style":960},[572,2646],{"className":2647,"style":901},[649],[572,2649,2651],{"className":2650},[622],[572,2652,739],{"className":2653},[622],[572,2655,865],{"className":2656},[864],[572,2658,2660],{"className":2659},[638],[572,2661,2664],{"className":2662,"style":2663},[642],"height:0.686em;",[572,2665],{},[572,2667],{"className":2668},[946,881],[572,2670],{"className":2671,"style":1020},[1019],[572,2673,735],{"className":2674},[1003],[572,2676],{"className":2677,"style":1020},[1019],[572,2679,2681,2684,2746,2749,2752],{"className":2680},[613],[572,2682],{"className":2683,"style":2604},[617],[572,2685,2687,2690,2743],{"className":2686},[622],[572,2688],{"className":2689},[823,881],[572,2691,2693],{"className":2692},[720],[572,2694,2696,2735],{"className":2695},[634,832],[572,2697,2699,2732],{"className":2698},[638],[572,2700,2702,2713,2721],{"className":2701,"style":2623},[642],[572,2703,2704,2707],{"style":897},[572,2705],{"className":2706,"style":901},[649],[572,2708,2710],{"className":2709},[622],[572,2711,2425],{"className":2712},[622],[572,2714,2715,2718],{"style":949},[572,2716],{"className":2717,"style":901},[649],[572,2719],{"className":2720,"style":957},[956],[572,2722,2723,2726],{"style":960},[572,2724],{"className":2725,"style":901},[649],[572,2727,2729],{"className":2728},[622],[572,2730,739],{"className":2731},[622],[572,2733,865],{"className":2734},[864],[572,2736,2738],{"className":2737},[638],[572,2739,2741],{"className":2740,"style":2663},[642],[572,2742],{},[572,2744],{"className":2745},[946,881],[572,2747],{"className":2748,"style":1020},[1019],[572,2750,735],{"className":2751},[1003],[572,2753],{"className":2754,"style":1020},[1019],[572,2756,2758,2761,2823,2826,2829],{"className":2757},[613],[572,2759],{"className":2760,"style":2604},[617],[572,2762,2764,2767,2820],{"className":2763},[622],[572,2765],{"className":2766},[823,881],[572,2768,2770],{"className":2769},[720],[572,2771,2773,2812],{"className":2772},[634,832],[572,2774,2776,2809],{"className":2775},[638],[572,2777,2779,2790,2798],{"className":2778,"style":2623},[642],[572,2780,2781,2784],{"style":897},[572,2782],{"className":2783,"style":901},[649],[572,2785,2787],{"className":2786},[622],[572,2788,2512],{"className":2789},[622],[572,2791,2792,2795],{"style":949},[572,2793],{"className":2794,"style":901},[649],[572,2796],{"className":2797,"style":957},[956],[572,2799,2800,2803],{"style":960},[572,2801],{"className":2802,"style":901},[649],[572,2804,2806],{"className":2805},[622],[572,2807,739],{"className":2808},[622],[572,2810,865],{"className":2811},[864],[572,2813,2815],{"className":2814},[638],[572,2816,2818],{"className":2817,"style":2663},[642],[572,2819],{},[572,2821],{"className":2822},[946,881],[572,2824],{"className":2825,"style":1020},[1019],[572,2827,735],{"className":2828},[1003],[572,2830],{"className":2831,"style":1020},[1019],[572,2833,2835,2838,2900,2903,2906],{"className":2834},[613],[572,2836],{"className":2837,"style":2604},[617],[572,2839,2841,2844,2897],{"className":2840},[622],[572,2842],{"className":2843},[823,881],[572,2845,2847],{"className":2846},[720],[572,2848,2850,2889],{"className":2849},[634,832],[572,2851,2853,2886],{"className":2852},[638],[572,2854,2856,2867,2875],{"className":2855,"style":2623},[642],[572,2857,2858,2861],{"style":897},[572,2859],{"className":2860,"style":901},[649],[572,2862,2864],{"className":2863},[622],[572,2865,2521],{"className":2866},[622],[572,2868,2869,2872],{"style":949},[572,2870],{"className":2871,"style":901},[649],[572,2873],{"className":2874,"style":957},[956],[572,2876,2877,2880],{"style":960},[572,2878],{"className":2879,"style":901},[649],[572,2881,2883],{"className":2882},[622],[572,2884,739],{"className":2885},[622],[572,2887,865],{"className":2888},[864],[572,2890,2892],{"className":2891},[638],[572,2893,2895],{"className":2894,"style":2663},[642],[572,2896],{},[572,2898],{"className":2899},[946,881],[572,2901],{"className":2902,"style":1020},[1019],[572,2904,735],{"className":2905},[1003],[572,2907],{"className":2908,"style":1020},[1019],[572,2910,2912,2915,2977,2980,2983],{"className":2911},[613],[572,2913],{"className":2914,"style":2604},[617],[572,2916,2918,2921,2974],{"className":2917},[622],[572,2919],{"className":2920},[823,881],[572,2922,2924],{"className":2923},[720],[572,2925,2927,2966],{"className":2926},[634,832],[572,2928,2930,2963],{"className":2929},[638],[572,2931,2933,2944,2952],{"className":2932,"style":2623},[642],[572,2934,2935,2938],{"style":897},[572,2936],{"className":2937,"style":901},[649],[572,2939,2941],{"className":2940},[622],[572,2942,2530],{"className":2943},[622],[572,2945,2946,2949],{"style":949},[572,2947],{"className":2948,"style":901},[649],[572,2950],{"className":2951,"style":957},[956],[572,2953,2954,2957],{"style":960},[572,2955],{"className":2956,"style":901},[649],[572,2958,2960],{"className":2959},[622],[572,2961,739],{"className":2962},[622],[572,2964,865],{"className":2965},[864],[572,2967,2969],{"className":2968},[638],[572,2970,2972],{"className":2971,"style":2663},[642],[572,2973],{},[572,2975],{"className":2976},[946,881],[572,2978],{"className":2979,"style":1089},[1019],[572,2981,2480],{"className":2982},[1093],[572,2984],{"className":2985,"style":1089},[1019],[572,2987,2989,2993,2996,3004],{"className":2988},[613],[572,2990],{"className":2991,"style":2992},[617],"height:0.8389em;vertical-align:-0.1944em;",[572,2994,2495],{"className":2995},[622],[572,2997,2999],{"className":2998},[622],[572,3000,3003],{"className":3001},[3002],"mpunct",",",[572,3005,3007],{"className":3006},[622],"7181",[564,3009,3010,3011,3073,3074,1893],{},"Der genaue Wert ist ",[572,3012,3014,3033],{"className":3013},[575],[572,3015,3017],{"className":3016},[579],[581,3018,3019],{"xmlns":583},[585,3020,3021,3030],{},[588,3022,3023,3025,3027],{},[594,3024,596],{},[716,3026,2480],{},[737,3028,3029],{},"2,7183",[601,3031,3032],{"encoding":603},"e \\approx 2{,}7183",[572,3034,3036,3054],{"className":3035,"ariaHidden":609},[608],[572,3037,3039,3042,3045,3048,3051],{"className":3038},[613],[572,3040],{"className":3041,"style":2548},[617],[572,3043,596],{"className":3044},[622,626],[572,3046],{"className":3047,"style":1089},[1019],[572,3049,2480],{"className":3050},[1093],[572,3052],{"className":3053,"style":1089},[1019],[572,3055,3057,3060,3063,3069],{"className":3056},[613],[572,3058],{"className":3059,"style":2992},[617],[572,3061,2495],{"className":3062},[622],[572,3064,3066],{"className":3065},[622],[572,3067,3003],{"className":3068},[3002],[572,3070,3072],{"className":3071},[622],"7183",". Das nächste Glied wäre ",[572,3075,3077,3109],{"className":3076},[575],[572,3078,3080],{"className":3079},[579],[581,3081,3082],{"xmlns":583},[585,3083,3084,3106],{},[588,3085,3086,3097,3099],{},[720,3087,3088,3090],{},[737,3089,739],{},[588,3091,3092,3095],{},[737,3093,3094],{},"7",[716,3096,759],{"stretchy":746},[716,3098,778],{},[720,3100,3101,3103],{},[737,3102,739],{},[737,3104,3105],{},"5040",[601,3107,3108],{"encoding":603},"\\frac{1}{7!} = \\frac{1}{5040}",[572,3110,3112,3200],{"className":3111,"ariaHidden":609},[608],[572,3113,3115,3119,3191,3194,3197],{"className":3114},[613],[572,3116],{"className":3117,"style":3118},[617],"height:1.1901em;vertical-align:-0.345em;",[572,3120,3122,3125,3188],{"className":3121},[622],[572,3123],{"className":3124},[823,881],[572,3126,3128],{"className":3127},[720],[572,3129,3131,3180],{"className":3130},[634,832],[572,3132,3134,3177],{"className":3133},[638],[572,3135,3138,3155,3163],{"className":3136,"style":3137},[642],"height:0.8451em;",[572,3139,3140,3143],{"style":1407},[572,3141],{"className":3142,"style":901},[649],[572,3144,3146],{"className":3145},[654,655,656,657],[572,3147,3149,3152],{"className":3148},[622,657],[572,3150,3094],{"className":3151},[622,657],[572,3153,759],{"className":3154},[946,657],[572,3156,3157,3160],{"style":949},[572,3158],{"className":3159,"style":901},[649],[572,3161],{"className":3162,"style":957},[956],[572,3164,3165,3168],{"style":1433},[572,3166],{"className":3167,"style":901},[649],[572,3169,3171],{"className":3170},[654,655,656,657],[572,3172,3174],{"className":3173},[622,657],[572,3175,739],{"className":3176},[622,657],[572,3178,865],{"className":3179},[864],[572,3181,3183],{"className":3182},[638],[572,3184,3186],{"className":3185,"style":1486},[642],[572,3187],{},[572,3189],{"className":3190},[946,881],[572,3192],{"className":3193,"style":1089},[1019],[572,3195,778],{"className":3196},[1093],[572,3198],{"className":3199,"style":1089},[1019],[572,3201,3203,3206],{"className":3202},[613],[572,3204],{"className":3205,"style":3118},[617],[572,3207,3209,3212,3271],{"className":3208},[622],[572,3210],{"className":3211},[823,881],[572,3213,3215],{"className":3214},[720],[572,3216,3218,3263],{"className":3217},[634,832],[572,3219,3221,3260],{"className":3220},[638],[572,3222,3224,3238,3246],{"className":3223,"style":3137},[642],[572,3225,3226,3229],{"style":1407},[572,3227],{"className":3228,"style":901},[649],[572,3230,3232],{"className":3231},[654,655,656,657],[572,3233,3235],{"className":3234},[622,657],[572,3236,3105],{"className":3237},[622,657],[572,3239,3240,3243],{"style":949},[572,3241],{"className":3242,"style":901},[649],[572,3244],{"className":3245,"style":957},[956],[572,3247,3248,3251],{"style":1433},[572,3249],{"className":3250,"style":901},[649],[572,3252,3254],{"className":3253},[654,655,656,657],[572,3255,3257],{"className":3256},[622,657],[572,3258,739],{"className":3259},[622,657],[572,3261,865],{"className":3262},[864],[572,3264,3266],{"className":3265},[638],[572,3267,3269],{"className":3268,"style":1486},[642],[572,3270],{},[572,3272],{"className":3273},[946,881],[564,3275,2325,3276,3338],{},[572,3277,3279,3298],{"className":3278},[575],[572,3280,3282],{"className":3281},[579],[581,3283,3284],{"xmlns":583},[585,3285,3286,3295],{},[588,3287,3288,3290,3292],{},[594,3289,599],{},[716,3291,778],{},[737,3293,3294],{},"0,5",[601,3296,3297],{"encoding":603},"x = 0{,}5",[572,3299,3301,3319],{"className":3300,"ariaHidden":609},[608],[572,3302,3304,3307,3310,3313,3316],{"className":3303},[613],[572,3305],{"className":3306,"style":691},[617],[572,3308,599],{"className":3309},[622,626],[572,3311],{"className":3312,"style":1089},[1019],[572,3314,778],{"className":3315},[1093],[572,3317],{"className":3318,"style":1089},[1019],[572,3320,3322,3325,3328,3334],{"className":3321},[613],[572,3323],{"className":3324,"style":2992},[617],[572,3326,802],{"className":3327},[622],[572,3329,3331],{"className":3330},[622],[572,3332,3003],{"className":3333},[3002],[572,3335,3337],{"className":3336},[622],"5"," mit vier Gliedern:",[572,3340,3342],{"className":3341},[699],[572,3343,3345,3404],{"className":3344},[575],[572,3346,3348],{"className":3347},[579],[581,3349,3350],{"xmlns":583,"display":708},[585,3351,3352,3401],{},[588,3353,3354,3360,3362,3364,3366,3368,3370,3377,3379,3386,3388,3396,3398],{},[591,3355,3356,3358],{},[594,3357,596],{},[737,3359,3294],{},[716,3361,2480],{},[737,3363,739],{},[716,3365,735],{},[737,3367,3294],{},[716,3369,735],{},[720,3371,3372,3375],{},[737,3373,3374],{},"0,25",[737,3376,2495],{},[716,3378,735],{},[720,3380,3381,3384],{},[737,3382,3383],{},"0,125",[737,3385,2425],{},[716,3387,778],{},[720,3389,3390,3393],{},[737,3391,3392],{},"79",[737,3394,3395],{},"48",[716,3397,2480],{},[737,3399,3400],{},"1,6458",[601,3402,3403],{"encoding":603},"e^{0{,}5} \\approx 1 + 0{,}5 + \\frac{0{,}25}{2} + \\frac{0{,}125}{6} = \\frac{79}{48} \\approx 1{,}6458",[572,3405,3407,3465,3483,3510,3597,3684,3761],{"className":3406,"ariaHidden":609},[608],[572,3408,3410,3414,3456,3459,3462],{"className":3409},[613],[572,3411],{"className":3412,"style":3413},[617],"height:0.8641em;",[572,3415,3417,3420],{"className":3416},[622],[572,3418,596],{"className":3419},[622,626],[572,3421,3423],{"className":3422},[630],[572,3424,3426],{"className":3425},[634],[572,3427,3429],{"className":3428},[638],[572,3430,3432],{"className":3431,"style":3413},[642],[572,3433,3435,3438],{"style":3434},"top:-3.113em;margin-right:0.05em;",[572,3436],{"className":3437,"style":650},[649],[572,3439,3441],{"className":3440},[654,655,656,657],[572,3442,3444,3447,3453],{"className":3443},[622,657],[572,3445,802],{"className":3446},[622,657],[572,3448,3450],{"className":3449},[622,657],[572,3451,3003],{"className":3452},[3002,657],[572,3454,3337],{"className":3455},[622,657],[572,3457],{"className":3458,"style":1089},[1019],[572,3460,2480],{"className":3461},[1093],[572,3463],{"className":3464,"style":1089},[1019],[572,3466,3468,3471,3474,3477,3480],{"className":3467},[613],[572,3469],{"className":3470,"style":2567},[617],[572,3472,739],{"className":3473},[622],[572,3475],{"className":3476,"style":1020},[1019],[572,3478,735],{"className":3479},[1003],[572,3481],{"className":3482,"style":1020},[1019],[572,3484,3486,3489,3492,3498,3501,3504,3507],{"className":3485},[613],[572,3487],{"className":3488,"style":2992},[617],[572,3490,802],{"className":3491},[622],[572,3493,3495],{"className":3494},[622],[572,3496,3003],{"className":3497},[3002],[572,3499,3337],{"className":3500},[622],[572,3502],{"className":3503,"style":1020},[1019],[572,3505,735],{"className":3506},[1003],[572,3508],{"className":3509,"style":1020},[1019],[572,3511,3513,3516,3588,3591,3594],{"className":3512},[613],[572,3514],{"className":3515,"style":2604},[617],[572,3517,3519,3522,3585],{"className":3518},[622],[572,3520],{"className":3521},[823,881],[572,3523,3525],{"className":3524},[720],[572,3526,3528,3577],{"className":3527},[634,832],[572,3529,3531,3574],{"className":3530},[638],[572,3532,3534,3545,3553],{"className":3533,"style":2623},[642],[572,3535,3536,3539],{"style":897},[572,3537],{"className":3538,"style":901},[649],[572,3540,3542],{"className":3541},[622],[572,3543,2495],{"className":3544},[622],[572,3546,3547,3550],{"style":949},[572,3548],{"className":3549,"style":901},[649],[572,3551],{"className":3552,"style":957},[956],[572,3554,3555,3558],{"style":960},[572,3556],{"className":3557,"style":901},[649],[572,3559,3561,3564,3570],{"className":3560},[622],[572,3562,802],{"className":3563},[622],[572,3565,3567],{"className":3566},[622],[572,3568,3003],{"className":3569},[3002],[572,3571,3573],{"className":3572},[622],"25",[572,3575,865],{"className":3576},[864],[572,3578,3580],{"className":3579},[638],[572,3581,3583],{"className":3582,"style":2663},[642],[572,3584],{},[572,3586],{"className":3587},[946,881],[572,3589],{"className":3590,"style":1020},[1019],[572,3592,735],{"className":3593},[1003],[572,3595],{"className":3596,"style":1020},[1019],[572,3598,3600,3603,3675,3678,3681],{"className":3599},[613],[572,3601],{"className":3602,"style":2604},[617],[572,3604,3606,3609,3672],{"className":3605},[622],[572,3607],{"className":3608},[823,881],[572,3610,3612],{"className":3611},[720],[572,3613,3615,3664],{"className":3614},[634,832],[572,3616,3618,3661],{"className":3617},[638],[572,3619,3621,3632,3640],{"className":3620,"style":2623},[642],[572,3622,3623,3626],{"style":897},[572,3624],{"className":3625,"style":901},[649],[572,3627,3629],{"className":3628},[622],[572,3630,2425],{"className":3631},[622],[572,3633,3634,3637],{"style":949},[572,3635],{"className":3636,"style":901},[649],[572,3638],{"className":3639,"style":957},[956],[572,3641,3642,3645],{"style":960},[572,3643],{"className":3644,"style":901},[649],[572,3646,3648,3651,3657],{"className":3647},[622],[572,3649,802],{"className":3650},[622],[572,3652,3654],{"className":3653},[622],[572,3655,3003],{"className":3656},[3002],[572,3658,3660],{"className":3659},[622],"125",[572,3662,865],{"className":3663},[864],[572,3665,3667],{"className":3666},[638],[572,3668,3670],{"className":3669,"style":2663},[642],[572,3671],{},[572,3673],{"className":3674},[946,881],[572,3676],{"className":3677,"style":1089},[1019],[572,3679,778],{"className":3680},[1093],[572,3682],{"className":3683,"style":1089},[1019],[572,3685,3687,3690,3752,3755,3758],{"className":3686},[613],[572,3688],{"className":3689,"style":2604},[617],[572,3691,3693,3696,3749],{"className":3692},[622],[572,3694],{"className":3695},[823,881],[572,3697,3699],{"className":3698},[720],[572,3700,3702,3741],{"className":3701},[634,832],[572,3703,3705,3738],{"className":3704},[638],[572,3706,3708,3719,3727],{"className":3707,"style":2623},[642],[572,3709,3710,3713],{"style":897},[572,3711],{"className":3712,"style":901},[649],[572,3714,3716],{"className":3715},[622],[572,3717,3395],{"className":3718},[622],[572,3720,3721,3724],{"style":949},[572,3722],{"className":3723,"style":901},[649],[572,3725],{"className":3726,"style":957},[956],[572,3728,3729,3732],{"style":960},[572,3730],{"className":3731,"style":901},[649],[572,3733,3735],{"className":3734},[622],[572,3736,3392],{"className":3737},[622],[572,3739,865],{"className":3740},[864],[572,3742,3744],{"className":3743},[638],[572,3745,3747],{"className":3746,"style":2663},[642],[572,3748],{},[572,3750],{"className":3751},[946,881],[572,3753],{"className":3754,"style":1089},[1019],[572,3756,2480],{"className":3757},[1093],[572,3759],{"className":3760,"style":1089},[1019],[572,3762,3764,3767,3770,3776],{"className":3763},[613],[572,3765],{"className":3766,"style":2992},[617],[572,3768,739],{"className":3769},[622],[572,3771,3773],{"className":3772},[622],[572,3774,3003],{"className":3775},[3002],[572,3777,3779],{"className":3778},[622],"6458",[564,3781,3010,3782,1893],{},[572,3783,3785,3808],{"className":3784},[575],[572,3786,3788],{"className":3787},[579],[581,3789,3790],{"xmlns":583},[585,3791,3792,3805],{},[588,3793,3794,3800,3802],{},[591,3795,3796,3798],{},[594,3797,596],{},[737,3799,3294],{},[716,3801,2480],{},[737,3803,3804],{},"1,6487",[601,3806,3807],{"encoding":603},"e^{0{,}5} \\approx 1{,}6487",[572,3809,3811,3868],{"className":3810,"ariaHidden":609},[608],[572,3812,3814,3818,3859,3862,3865],{"className":3813},[613],[572,3815],{"className":3816,"style":3817},[617],"height:0.8141em;",[572,3819,3821,3824],{"className":3820},[622],[572,3822,596],{"className":3823},[622,626],[572,3825,3827],{"className":3826},[630],[572,3828,3830],{"className":3829},[634],[572,3831,3833],{"className":3832},[638],[572,3834,3836],{"className":3835,"style":3817},[642],[572,3837,3838,3841],{"style":645},[572,3839],{"className":3840,"style":650},[649],[572,3842,3844],{"className":3843},[654,655,656,657],[572,3845,3847,3850,3856],{"className":3846},[622,657],[572,3848,802],{"className":3849},[622,657],[572,3851,3853],{"className":3852},[622,657],[572,3854,3003],{"className":3855},[3002,657],[572,3857,3337],{"className":3858},[622,657],[572,3860],{"className":3861,"style":1089},[1019],[572,3863,2480],{"className":3864},[1093],[572,3866],{"className":3867,"style":1089},[1019],[572,3869,3871,3874,3877,3883],{"className":3870},[613],[572,3872],{"className":3873,"style":2992},[617],[572,3875,739],{"className":3876},[622],[572,3878,3880],{"className":3879},[622],[572,3881,3003],{"className":3882},[3002],[572,3884,3886],{"className":3885},[622],"6487",[564,3888,2325,3889,3946,3947,1893],{},[572,3890,3892,3913],{"className":3891},[575],[572,3893,3895],{"className":3894},[579],[581,3896,3897],{"xmlns":583},[585,3898,3899,3910],{},[588,3900,3901,3903,3905,3908],{},[594,3902,599],{},[716,3904,778],{},[716,3906,3907],{},"−",[737,3909,739],{},[601,3911,3912],{"encoding":603},"x = -1",[572,3914,3916,3934],{"className":3915,"ariaHidden":609},[608],[572,3917,3919,3922,3925,3928,3931],{"className":3918},[613],[572,3920],{"className":3921,"style":691},[617],[572,3923,599],{"className":3924},[622,626],[572,3926],{"className":3927,"style":1089},[1019],[572,3929,778],{"className":3930},[1093],[572,3932],{"className":3933,"style":1089},[1019],[572,3935,3937,3940,3943],{"className":3936},[613],[572,3938],{"className":3939,"style":2567},[617],[572,3941,3907],{"className":3942},[622],[572,3944,739],{"className":3945},[622]," wechseln die Vorzeichen, und die Reihe konvergiert gegen ",[572,3948,3950,3977],{"className":3949},[575],[572,3951,3953],{"className":3952},[579],[581,3954,3955],{"xmlns":583},[585,3956,3957,3974],{},[588,3958,3959,3969,3971],{},[591,3960,3961,3963],{},[594,3962,596],{},[588,3964,3965,3967],{},[716,3966,3907],{},[737,3968,739],{},[716,3970,2480],{},[737,3972,3973],{},"0,3679",[601,3975,3976],{"encoding":603},"e^{-1} \\approx 0{,}3679",[572,3978,3980,4030],{"className":3979,"ariaHidden":609},[608],[572,3981,3983,3986,4021,4024,4027],{"className":3982},[613],[572,3984],{"className":3985,"style":3817},[617],[572,3987,3989,3992],{"className":3988},[622],[572,3990,596],{"className":3991},[622,626],[572,3993,3995],{"className":3994},[630],[572,3996,3998],{"className":3997},[634],[572,3999,4001],{"className":4000},[638],[572,4002,4004],{"className":4003,"style":3817},[642],[572,4005,4006,4009],{"style":645},[572,4007],{"className":4008,"style":650},[649],[572,4010,4012],{"className":4011},[654,655,656,657],[572,4013,4015,4018],{"className":4014},[622,657],[572,4016,3907],{"className":4017},[622,657],[572,4019,739],{"className":4020},[622,657],[572,4022],{"className":4023,"style":1089},[1019],[572,4025,2480],{"className":4026},[1093],[572,4028],{"className":4029,"style":1089},[1019],[572,4031,4033,4036,4039,4045],{"className":4032},[613],[572,4034],{"className":4035,"style":2992},[617],[572,4037,802],{"className":4038},[622],[572,4040,4042],{"className":4041},[622],[572,4043,3003],{"className":4044},[3002],[572,4046,4048],{"className":4047},[622],"3679",[559,4050,4052],{"id":4051},"typische-fehler","Typische Fehler",[4054,4055,4056,4192,4328,4472],"ul",{},[4057,4058,4059,4060,4128,4129,4191],"li",{},"Die Fakultät im Nenner weglassen. ",[572,4061,4063,4083],{"className":4062},[575],[572,4064,4066],{"className":4065},[579],[581,4067,4068],{"xmlns":583},[585,4069,4070,4080],{},[588,4071,4072,4074],{},[716,4073,1246],{},[591,4075,4076,4078],{},[594,4077,599],{},[594,4079,732],{},[601,4081,4082],{"encoding":603},"\\sum x^k",[572,4084,4086],{"className":4085,"ariaHidden":609},[608],[572,4087,4089,4093,4096,4099],{"className":4088},[613],[572,4090],{"className":4091,"style":4092},[617],"height:1.0991em;vertical-align:-0.25em;",[572,4094,1246],{"className":4095,"style":1323},[1288,1321,1322],[572,4097],{"className":4098,"style":1385},[1019],[572,4100,4102,4105],{"className":4101},[622],[572,4103,599],{"className":4104},[622,626],[572,4106,4108],{"className":4107},[630],[572,4109,4111],{"className":4110},[634],[572,4112,4114],{"className":4113},[638],[572,4115,4117],{"className":4116,"style":985},[642],[572,4118,4119,4122],{"style":645},[572,4120],{"className":4121,"style":650},[649],[572,4123,4125],{"className":4124},[654,655,656,657],[572,4126,732],{"className":4127,"style":936},[622,626,657]," ist die geometrische Reihe, die nur für ",[572,4130,4132,4155],{"className":4131},[575],[572,4133,4135],{"className":4134},[579],[581,4136,4137],{"xmlns":583},[585,4138,4139,4152],{},[588,4140,4141,4143,4145,4147,4150],{},[594,4142,718],{"mathvariant":742},[594,4144,599],{},[594,4146,718],{"mathvariant":742},[716,4148,4149],{},"\u003C",[737,4151,739],{},[601,4153,4154],{"encoding":603},"|x| \u003C 1",[572,4156,4158,4182],{"className":4157,"ariaHidden":609},[608],[572,4159,4161,4164,4167,4170,4173,4176,4179],{"className":4160},[613],[572,4162],{"className":4163,"style":1284},[617],[572,4165,718],{"className":4166},[622],[572,4168,599],{"className":4169},[622,626],[572,4171,718],{"className":4172},[622],[572,4174],{"className":4175,"style":1089},[1019],[572,4177,4149],{"className":4178},[1093],[572,4180],{"className":4181,"style":1089},[1019],[572,4183,4185,4188],{"className":4184},[613],[572,4186],{"className":4187,"style":1201},[617],[572,4189,739],{"className":4190},[622]," konvergiert.",[4057,4193,4194,4195,4246,4247,4298,4299,4327],{},"Bei ",[572,4196,4198,4216],{"className":4197},[575],[572,4199,4201],{"className":4200},[579],[581,4202,4203],{"xmlns":583},[585,4204,4205,4213],{},[588,4206,4207,4209,4211],{},[594,4208,732],{},[716,4210,778],{},[737,4212,739],{},[601,4214,4215],{"encoding":603},"k = 1",[572,4217,4219,4237],{"className":4218,"ariaHidden":609},[608],[572,4220,4222,4225,4228,4231,4234],{"className":4221},[613],[572,4223],{"className":4224,"style":2438},[617],[572,4226,732],{"className":4227,"style":936},[622,626],[572,4229],{"className":4230,"style":1089},[1019],[572,4232,778],{"className":4233},[1093],[572,4235],{"className":4236,"style":1089},[1019],[572,4238,4240,4243],{"className":4239},[613],[572,4241],{"className":4242,"style":1201},[617],[572,4244,739],{"className":4245},[622]," statt bei ",[572,4248,4250,4268],{"className":4249},[575],[572,4251,4253],{"className":4252},[579],[581,4254,4255],{"xmlns":583},[585,4256,4257,4265],{},[588,4258,4259,4261,4263],{},[594,4260,732],{},[716,4262,778],{},[737,4264,802],{},[601,4266,4267],{"encoding":603},"k = 0",[572,4269,4271,4289],{"className":4270,"ariaHidden":609},[608],[572,4272,4274,4277,4280,4283,4286],{"className":4273},[613],[572,4275],{"className":4276,"style":2438},[617],[572,4278,732],{"className":4279,"style":936},[622,626],[572,4281],{"className":4282,"style":1089},[1019],[572,4284,778],{"className":4285},[1093],[572,4287],{"className":4288,"style":1089},[1019],[572,4290,4292,4295],{"className":4291},[613],[572,4293],{"className":4294,"style":1201},[617],[572,4296,802],{"className":4297},[622]," beginnen und so das Glied ",[572,4300,4302,4315],{"className":4301},[575],[572,4303,4305],{"className":4304},[579],[581,4306,4307],{"xmlns":583},[585,4308,4309,4313],{},[588,4310,4311],{},[737,4312,739],{},[601,4314,739],{"encoding":603},[572,4316,4318],{"className":4317,"ariaHidden":609},[608],[572,4319,4321,4324],{"className":4320},[613],[572,4322],{"className":4323,"style":1201},[617],[572,4325,739],{"className":4326},[622]," verlieren.",[4057,4329,4330,4386,4387,4443,4444,1893],{},[572,4331,4333,4353],{"className":4332},[575],[572,4334,4336],{"className":4335},[579],[581,4337,4338],{"xmlns":583},[585,4339,4340,4350],{},[588,4341,4342,4344,4346,4348],{},[737,4343,802],{},[716,4345,759],{"stretchy":746},[716,4347,778],{},[737,4349,802],{},[601,4351,4352],{"encoding":603},"0! = 0",[572,4354,4356,4377],{"className":4355,"ariaHidden":609},[608],[572,4357,4359,4362,4365,4368,4371,4374],{"className":4358},[613],[572,4360],{"className":4361,"style":2438},[617],[572,4363,802],{"className":4364},[622],[572,4366,759],{"className":4367},[946],[572,4369],{"className":4370,"style":1089},[1019],[572,4372,778],{"className":4373},[1093],[572,4375],{"className":4376,"style":1089},[1019],[572,4378,4380,4383],{"className":4379},[613],[572,4381],{"className":4382,"style":1201},[617],[572,4384,802],{"className":4385},[622]," setzen. Richtig ist ",[572,4388,4390,4410],{"className":4389},[575],[572,4391,4393],{"className":4392},[579],[581,4394,4395],{"xmlns":583},[585,4396,4397,4407],{},[588,4398,4399,4401,4403,4405],{},[737,4400,802],{},[716,4402,759],{"stretchy":746},[716,4404,778],{},[737,4406,739],{},[601,4408,4409],{"encoding":603},"0! = 1",[572,4411,4413,4434],{"className":4412,"ariaHidden":609},[608],[572,4414,4416,4419,4422,4425,4428,4431],{"className":4415},[613],[572,4417],{"className":4418,"style":2438},[617],[572,4420,802],{"className":4421},[622],[572,4423,759],{"className":4424},[946],[572,4426],{"className":4427,"style":1089},[1019],[572,4429,778],{"className":4430},[1093],[572,4432],{"className":4433,"style":1089},[1019],[572,4435,4437,4440],{"className":4436},[613],[572,4438],{"className":4439,"style":1201},[617],[572,4441,739],{"className":4442},[622],", sonst entsteht eine Division durch ",[572,4445,4447,4460],{"className":4446},[575],[572,4448,4450],{"className":4449},[579],[581,4451,4452],{"xmlns":583},[585,4453,4454,4458],{},[588,4455,4456],{},[737,4457,802],{},[601,4459,802],{"encoding":603},[572,4461,4463],{"className":4462,"ariaHidden":609},[608],[572,4464,4466,4469],{"className":4465},[613],[572,4467],{"className":4468,"style":1201},[617],[572,4470,802],{"className":4471},[622],[4057,4473,4474,4475,4514,4515,4543,4544,4582],{},"Für großes ",[572,4476,4478,4496],{"className":4477},[575],[572,4479,4481],{"className":4480},[579],[581,4482,4483],{"xmlns":583},[585,4484,4485,4493],{},[588,4486,4487,4489,4491],{},[594,4488,718],{"mathvariant":742},[594,4490,599],{},[594,4492,718],{"mathvariant":742},[601,4494,4495],{"encoding":603},"|x|",[572,4497,4499],{"className":4498,"ariaHidden":609},[608],[572,4500,4502,4505,4508,4511],{"className":4501},[613],[572,4503],{"className":4504,"style":1284},[617],[572,4506,718],{"className":4507},[622],[572,4509,599],{"className":4510},[622,626],[572,4512,718],{"className":4513},[622]," wenige Glieder für ausreichend halten. Die Glieder werden erst klein, wenn ",[572,4516,4518,4531],{"className":4517},[575],[572,4519,4521],{"className":4520},[579],[581,4522,4523],{"xmlns":583},[585,4524,4525,4529],{},[588,4526,4527],{},[594,4528,732],{},[601,4530,732],{"encoding":603},[572,4532,4534],{"className":4533,"ariaHidden":609},[608],[572,4535,4537,4540],{"className":4536},[613],[572,4538],{"className":4539,"style":2438},[617],[572,4541,732],{"className":4542,"style":936},[622,626]," deutlich größer als ",[572,4545,4547,4564],{"className":4546},[575],[572,4548,4550],{"className":4549},[579],[581,4551,4552],{"xmlns":583},[585,4553,4554,4562],{},[588,4555,4556,4558,4560],{},[594,4557,718],{"mathvariant":742},[594,4559,599],{},[594,4561,718],{"mathvariant":742},[601,4563,4495],{"encoding":603},[572,4565,4567],{"className":4566,"ariaHidden":609},[608],[572,4568,4570,4573,4576,4579],{"className":4569},[613],[572,4571],{"className":4572,"style":1284},[617],[572,4574,718],{"className":4575},[622],[572,4577,599],{"className":4578},[622,626],[572,4580,718],{"className":4581},[622]," ist.",{"title":4584,"searchDepth":4585,"depth":4585,"links":4586},"",2,[4587,4588,4589],{"id":561,"depth":4585,"text":562},{"id":2321,"depth":4585,"text":2322},{"id":4051,"depth":4585,"text":4052},[4591,4594,4599,4602,4605,4608,4611,4614,4617,4620],{"lhs":4592,"rhs":4593},"sum(x.^(0:30) .\u002F (0:30)!)","exp(x)",{"lhs":4595,"rhs":4596,"where":4597},"(k + 1)*x^k\u002F(k + 1)!","x^k\u002Fk!",{"k":4598},4,{"lhs":4600,"rhs":4601},"round(sum(1 .\u002F (0:6)!), 4)","2.7181",{"lhs":4603,"rhs":4604},"round(exp(1), 4)","2.7183",{"lhs":4606,"rhs":4607},"1\u002F7!","1\u002F5040",{"lhs":4609,"rhs":4610},"1 + 0.5 + 0.5^2\u002F2 + 0.5^3\u002F6","79\u002F48",{"lhs":4612,"rhs":4613},"round(79\u002F48, 4)","1.6458",{"lhs":4615,"rhs":4616},"round(exp(0.5), 4)","1.6487",{"lhs":4618,"rhs":4619},"round(sum((-1).^(0:30) .\u002F (0:30)!), 6)","round(exp(-1), 6)",{"lhs":4621,"rhs":4622},"round(exp(-1), 4)","0.3679","x \\in \\mathbb{R}\\ (\\text{auch } x \\in \\mathbb{C})","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmtext> \u003C\u002Fmtext>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmtext>auch \u003C\u002Fmtext>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">C\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x \\in \\mathbb{R}\\ (\\text{auch } x \\in \\mathbb{C})\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\">x\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"mspace\"> \u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\">auch \u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">C\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","exponential-series","e^x = \\sum_{k=0}^{\\infty} \\frac{x^k}{k!} = 1 + x + \\frac{x^2}{2!} + \\frac{x^3}{3!} + \\ldots","\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>\u003Cmsup>\u003Cmi>e\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>=\u003C\u002Fmo>\u003Cmunderover>\u003Cmo>∑\u003C\u002Fmo>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmunderover>\u003Cmfrac>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmfrac>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmrow>\u003Cmn>2\u003C\u002Fmn>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>+\u003C\u002Fmo>\u003Cmfrac>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmrow>\u003Cmn>3\u003C\u002Fmn>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>+\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">e^x = \\sum_{k=0}^{\\infty} \\frac{x^k}{k!} = 1 + x + \\frac{x^2}{2!} + \\frac{x^3}{3!} + \\ldots\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:0.7144em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">e\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7144em;\">\u003Cspan style=\"top:-3.113em;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\">x\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:2.9535em;vertical-align:-1.3021em;\">\u003C\u002Fspan>\u003Cspan class=\"mop op-limits\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.6514em;\">\u003Cspan style=\"top:-1.8479em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mrel mtight\">=\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.05em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan>\u003Cspan class=\"mop op-symbol large-op\">∑\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-4.3em;margin-left:0em;\">\u003Cspan class=\"pstrut\" style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3021em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.5261em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mclose\">!\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\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8491em;\">\u003Cspan style=\"top:-3.063em;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\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\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:0.7278em;vertical-align:-0.0833em;\">\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>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\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:2.1771em;vertical-align:-0.686em;\">\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:1.4911em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mclose\">!\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\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose 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