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Deshalb kommen nur ",[568,937,938],{},"ungerade"," Potenzen vor, mit wechselndem Vorzeichen.",[564,941,942,943,946,947,978,979,1010,1011,1041],{},"Die Reihe konvergiert für ",[568,944,945],{},"jedes"," reelle ",[572,948,950,964],{"className":949},[575],[572,951,953],{"className":952},[579],[581,954,955],{"xmlns":583},[585,956,957,962],{},[588,958,959],{},[591,960,961],{},"x",[599,963,961],{"encoding":601},[572,965,967],{"className":966,"ariaHidden":607},[606],[572,968,970,974],{"className":969},[611],[572,971],{"className":972,"style":973},[615],"height:0.4306em;",[572,975,961],{"className":976},[653,977],"mathnormal"," (Konvergenzradius ",[572,980,982,998],{"className":981},[575],[572,983,985],{"className":984},[579],[581,986,987],{"xmlns":583},[585,988,989,995],{},[588,990,991],{},[591,992,994],{"mathvariant":993},"normal","∞",[599,996,997],{"encoding":601},"\\infty",[572,999,1001],{"className":1000,"ariaHidden":607},[606],[572,1002,1004,1007],{"className":1003},[611],[572,1005],{"className":1006,"style":973},[615],[572,1008,994],{"className":1009},[653],"), weil die Fakultät im Nenner schneller wächst als jede Potenz. Sie spiegelt wider, dass ",[572,1012,1014,1029],{"className":1013},[575],[572,1015,1017],{"className":1016},[579],[581,1018,1019],{"xmlns":583},[585,1020,1021,1027],{},[588,1022,1023,1025],{},[591,1024,593],{},[595,1026,597],{},[599,1028,602],{"encoding":601},[572,1030,1032],{"className":1031,"ariaHidden":607},[606],[572,1033,1035,1038],{"className":1034},[611],[572,1036],{"className":1037,"style":616},[615],[572,1039,593],{"className":1040},[620]," eine ungerade Funktion ist.",[564,1043,1044,1045,1073],{},"Für kleine ",[572,1046,1048,1061],{"className":1047},[575],[572,1049,1051],{"className":1050},[579],[581,1052,1053],{"xmlns":583},[585,1054,1055,1059],{},[588,1056,1057],{},[591,1058,961],{},[599,1060,961],{"encoding":601},[572,1062,1064],{"className":1063,"ariaHidden":607},[606],[572,1065,1067,1070],{"className":1066},[611],[572,1068],{"className":1069,"style":973},[615],[572,1071,961],{"className":1072},[653,977]," liefern schon die ersten Glieder gute Näherungen:",[1075,1076,1077,1149],"ul",{},[1078,1079,1080,1144,1145,1148],"li",{},[572,1081,1083,1106],{"className":1082},[575],[572,1084,1086],{"className":1085},[579],[581,1087,1088],{"xmlns":583},[585,1089,1090,1103],{},[588,1091,1092,1094,1096,1098,1101],{},[591,1093,593],{},[595,1095,597],{},[591,1097,961],{},[595,1099,1100],{},"≈",[591,1102,961],{},[599,1104,1105],{"encoding":601},"\\sin x \\approx x",[572,1107,1109,1135],{"className":1108,"ariaHidden":607},[606],[572,1110,1112,1115,1118,1121,1124,1128,1132],{"className":1111},[611],[572,1113],{"className":1114,"style":616},[615],[572,1116,593],{"className":1117},[620],[572,1119],{"className":1120,"style":781},[780],[572,1122,961],{"className":1123},[653,977],[572,1125],{"className":1126,"style":1127},[780],"margin-right:0.2778em;",[572,1129,1100],{"className":1130},[1131],"mrel",[572,1133],{"className":1134,"style":1127},[780],[572,1136,1138,1141],{"className":1137},[611],[572,1139],{"className":1140,"style":973},[615],[572,1142,961],{"className":1143},[653,977]," (",[568,1146,1147],{},"Kleinwinkelnäherung",", z.B. beim Fadenpendel).",[1078,1150,1151,1369],{},[572,1152,1154,1192],{"className":1153},[575],[572,1155,1157],{"className":1156},[579],[581,1158,1159],{"xmlns":583},[585,1160,1161,1189],{},[588,1162,1163,1165,1167,1169,1171,1173,1175],{},[591,1164,593],{},[595,1166,597],{},[591,1168,961],{},[595,1170,1100],{},[591,1172,961],{},[595,1174,744],{},[1176,1177,1178,1186],"mfrac",{},[1179,1180,1181,1183],"msup",{},[591,1182,961],{},[635,1184,1185],{},"3",[635,1187,1188],{},"6",[599,1190,1191],{"encoding":601},"\\sin x \\approx x - \\frac{x^3}{6}",[572,1193,1195,1219,1240],{"className":1194,"ariaHidden":607},[606],[572,1196,1198,1201,1204,1207,1210,1213,1216],{"className":1197},[611],[572,1199],{"className":1200,"style":616},[615],[572,1202,593],{"className":1203},[620],[572,1205],{"className":1206,"style":781},[780],[572,1208,961],{"className":1209},[653,977],[572,1211],{"className":1212,"style":1127},[780],[572,1214,1100],{"className":1215},[1131],[572,1217],{"className":1218,"style":1127},[780],[572,1220,1222,1226,1229,1233,1237],{"className":1221},[611],[572,1223],{"className":1224,"style":1225},[615],"height:0.6667em;vertical-align:-0.0833em;",[572,1227,961],{"className":1228},[653,977],[572,1230],{"className":1231,"style":1232},[780],"margin-right:0.2222em;",[572,1234,744],{"className":1235},[1236],"mbin",[572,1238],{"className":1239,"style":1232},[780],[572,1241,1243,1247],{"className":1242},[611],[572,1244],{"className":1245,"style":1246},[615],"height:1.3629em;vertical-align:-0.345em;",[572,1248,1250,1255,1365],{"className":1249},[653],[572,1251],{"className":1252},[1253,1254],"mopen","nulldelimiter",[572,1256,1258],{"className":1257},[1176],[572,1259,1263,1356],{"className":1260},[1261,1262],"vlist-t","vlist-t2",[572,1264,1267,1351],{"className":1265},[1266],"vlist-r",[572,1268,1272,1293,1304],{"className":1269,"style":1271},[1270],"vlist","height:1.0179em;",[572,1273,1275,1280],{"style":1274},"top:-2.655em;",[572,1276],{"className":1277,"style":1279},[1278],"pstrut","height:3em;",[572,1281,1287],{"className":1282},[1283,1284,1285,1286],"sizing","reset-size6","size3","mtight",[572,1288,1290],{"className":1289},[653,1286],[572,1291,1188],{"className":1292},[653,1286],[572,1294,1296,1299],{"style":1295},"top:-3.23em;",[572,1297],{"className":1298,"style":1279},[1278],[572,1300],{"className":1301,"style":1303},[1302],"frac-line","border-bottom-width:0.04em;",[572,1305,1307,1310],{"style":1306},"top:-3.394em;",[572,1308],{"className":1309,"style":1279},[1278],[572,1311,1313],{"className":1312},[1283,1284,1285,1286],[572,1314,1316],{"className":1315},[653,1286],[572,1317,1319,1322],{"className":1318},[653,1286],[572,1320,961],{"className":1321},[653,977,1286],[572,1323,1326],{"className":1324},[1325],"msupsub",[572,1327,1329],{"className":1328},[1261],[572,1330,1332],{"className":1331},[1266],[572,1333,1336],{"className":1334,"style":1335},[1270],"height:0.8913em;",[572,1337,1339,1343],{"style":1338},"top:-2.931em;margin-right:0.0714em;",[572,1340],{"className":1341,"style":1342},[1278],"height:2.5em;",[572,1344,1348],{"className":1345},[1283,1346,1347,1286],"reset-size3","size1",[572,1349,1185],{"className":1350},[653,1286],[572,1352,1355],{"className":1353},[1354],"vlist-s","​",[572,1357,1359],{"className":1358},[1266],[572,1360,1363],{"className":1361,"style":1362},[1270],"height:0.345em;",[572,1364],{},[572,1366],{"className":1367},[1368,1254],"mclose"," für etwas größere Winkel.",[564,1371,1372,1373,1437],{},"Weil die Reihe für ",[572,1374,1376,1400],{"className":1375},[575],[572,1377,1379],{"className":1378},[579],[581,1380,1381],{"xmlns":583},[585,1382,1383,1397],{},[588,1384,1385,1388,1390,1392,1395],{},[591,1386,1387],{"mathvariant":993},"∣",[591,1389,961],{},[591,1391,1387],{"mathvariant":993},[595,1393,1394],{},"≤",[635,1396,863],{},[599,1398,1399],{"encoding":601},"|x| \\leq 1",[572,1401,1403,1428],{"className":1402,"ariaHidden":607},[606],[572,1404,1406,1410,1413,1416,1419,1422,1425],{"className":1405},[611],[572,1407],{"className":1408,"style":1409},[615],"height:1em;vertical-align:-0.25em;",[572,1411,1387],{"className":1412},[653],[572,1414,961],{"className":1415},[653,977],[572,1417,1387],{"className":1418},[653],[572,1420],{"className":1421,"style":1127},[780],[572,1423,1394],{"className":1424},[1131],[572,1426],{"className":1427,"style":1127},[780],[572,1429,1431,1434],{"className":1430},[611],[572,1432],{"className":1433,"style":649},[615],[572,1435,863],{"className":1436},[653]," alternierend mit fallenden Gliedern ist, ist der Fehler beim Abbrechen höchstens so groß wie das erste weggelassene Glied.",[564,1439,1440,1441,1589],{},"Leitet man die Reihe gliedweise ab, erhält man die Kosinusreihe. Mit der Eulerschen Formel ",[572,1442,1444,1488],{"className":1443},[575],[572,1445,1447],{"className":1446},[579],[581,1448,1449],{"xmlns":583},[585,1450,1451,1485],{},[588,1452,1453,1465,1468,1470,1472,1474,1477,1479,1481,1483],{},[1179,1454,1455,1458],{},[591,1456,1457],{},"e",[588,1459,1460,1463],{},[591,1461,1462],{},"i",[591,1464,961],{},[595,1466,1467],{},"=",[591,1469,737],{},[595,1471,597],{},[591,1473,961],{},[595,1475,1476],{},"+",[591,1478,1462],{},[591,1480,593],{},[595,1482,597],{},[591,1484,961],{},[599,1486,1487],{"encoding":601},"e^{ix} = \\cos x + i \\sin x",[572,1489,1491,1544,1568],{"className":1490,"ariaHidden":607},[606],[572,1492,1494,1498,1535,1538,1541],{"className":1493},[611],[572,1495],{"className":1496,"style":1497},[615],"height:0.8247em;",[572,1499,1501,1504],{"className":1500},[653],[572,1502,1457],{"className":1503},[653,977],[572,1505,1507],{"className":1506},[1325],[572,1508,1510],{"className":1509},[1261],[572,1511,1513],{"className":1512},[1266],[572,1514,1516],{"className":1515,"style":1497},[1270],[572,1517,1519,1523],{"style":1518},"top:-3.063em;margin-right:0.05em;",[572,1520],{"className":1521,"style":1522},[1278],"height:2.7em;",[572,1524,1526],{"className":1525},[1283,1284,1285,1286],[572,1527,1529,1532],{"className":1528},[653,1286],[572,1530,1462],{"className":1531},[653,977,1286],[572,1533,961],{"className":1534},[653,977,1286],[572,1536],{"className":1537,"style":1127},[780],[572,1539,1467],{"className":1540},[1131],[572,1542],{"className":1543,"style":1127},[780],[572,1545,1547,1550,1553,1556,1559,1562,1565],{"className":1546},[611],[572,1548],{"className":1549,"style":1225},[615],[572,1551,737],{"className":1552},[620],[572,1554],{"className":1555,"style":781},[780],[572,1557,961],{"className":1558},[653,977],[572,1560],{"className":1561,"style":1232},[780],[572,1563,1476],{"className":1564},[1236],[572,1566],{"className":1567,"style":1232},[780],[572,1569,1571,1574,1577,1580,1583,1586],{"className":1570},[611],[572,1572],{"className":1573,"style":616},[615],[572,1575,1462],{"className":1576},[653,977],[572,1578],{"className":1579,"style":781},[780],[572,1581,593],{"className":1582},[620],[572,1584],{"className":1585,"style":781},[780],[572,1587,961],{"className":1588},[653,977]," ergibt sich die Sinusreihe als Imaginärteil der Exponentialreihe.",[559,1591,1593],{"id":1592},"beispiele","Beispiele",[564,1595,1596,1814,1815],{},[572,1597,1599,1636],{"className":1598},[575],[572,1600,1602],{"className":1601},[579],[581,1603,1604],{"xmlns":583},[585,1605,1606,1633],{},[588,1607,1608,1610,1612,1615,1617,1619,1621,1628,1630],{},[591,1609,593],{},[595,1611,597],{},[635,1613,1614],{},"0,1",[595,1616,1100],{},[635,1618,1614],{},[595,1620,744],{},[1176,1622,1623,1626],{},[635,1624,1625],{},"0,001",[635,1627,1188],{},[595,1629,1100],{},[635,1631,1632],{},"0,0998333",[599,1634,1635],{"encoding":601},"\\sin 0{,}1 \\approx 0{,}1 - \\frac{0{,}001}{6} \\approx 0{,}0998333",[572,1637,1639,1672,1699,1795],{"className":1638,"ariaHidden":607},[606],[572,1640,1642,1645,1648,1651,1654,1660,1663,1666,1669],{"className":1641},[611],[572,1643],{"className":1644,"style":769},[615],[572,1646,593],{"className":1647},[620],[572,1649],{"className":1650,"style":781},[780],[572,1652,637],{"className":1653},[653],[572,1655,1657],{"className":1656},[653],[572,1658,734],{"className":1659},[776],[572,1661,863],{"className":1662},[653],[572,1664],{"className":1665,"style":1127},[780],[572,1667,1100],{"className":1668},[1131],[572,1670],{"className":1671,"style":1127},[780],[572,1673,1675,1678,1681,1687,1690,1693,1696],{"className":1674},[611],[572,1676],{"className":1677,"style":891},[615],[572,1679,637],{"className":1680},[653],[572,1682,1684],{"className":1683},[653],[572,1685,734],{"className":1686},[776],[572,1688,863],{"className":1689},[653],[572,1691],{"className":1692,"style":1232},[780],[572,1694,744],{"className":1695},[1236],[572,1697],{"className":1698,"style":1232},[780],[572,1700,1702,1706,1786,1789,1792],{"className":1701},[611],[572,1703],{"className":1704,"style":1705},[615],"height:1.2422em;vertical-align:-0.345em;",[572,1707,1709,1712,1783],{"className":1708},[653],[572,1710],{"className":1711},[1253,1254],[572,1713,1715],{"className":1714},[1176],[572,1716,1718,1775],{"className":1717},[1261,1262],[572,1719,1721,1772],{"className":1720},[1266],[572,1722,1725,1739,1747],{"className":1723,"style":1724},[1270],"height:0.8972em;",[572,1726,1727,1730],{"style":1274},[572,1728],{"className":1729,"style":1279},[1278],[572,1731,1733],{"className":1732},[1283,1284,1285,1286],[572,1734,1736],{"className":1735},[653,1286],[572,1737,1188],{"className":1738},[653,1286],[572,1740,1741,1744],{"style":1295},[572,1742],{"className":1743,"style":1279},[1278],[572,1745],{"className":1746,"style":1303},[1302],[572,1748,1750,1753],{"style":1749},"top:-3.4461em;",[572,1751],{"className":1752,"style":1279},[1278],[572,1754,1756],{"className":1755},[1283,1284,1285,1286],[572,1757,1759,1762,1768],{"className":1758},[653,1286],[572,1760,637],{"className":1761},[653,1286],[572,1763,1765],{"className":1764},[653,1286],[572,1766,734],{"className":1767},[776,1286],[572,1769,1771],{"className":1770},[653,1286],"001",[572,1773,1355],{"className":1774},[1354],[572,1776,1778],{"className":1777},[1266],[572,1779,1781],{"className":1780,"style":1362},[1270],[572,1782],{},[572,1784],{"className":1785},[1368,1254],[572,1787],{"className":1788,"style":1127},[780],[572,1790,1100],{"className":1791},[1131],[572,1793],{"className":1794,"style":1127},[780],[572,1796,1798,1801,1804,1810],{"className":1797},[611],[572,1799],{"className":1800,"style":891},[615],[572,1802,637],{"className":1803},[653],[572,1805,1807],{"className":1806},[653],[572,1808,734],{"className":1809},[776],[572,1811,1813],{"className":1812},[653],"0998333",". Der genaue Wert ist ",[572,1816,1818,1835],{"className":1817},[575],[572,1819,1821],{"className":1820},[579],[581,1822,1823],{"xmlns":583},[585,1824,1825,1832],{},[588,1826,1827,1830],{},[635,1828,1829],{},"0,0998334",[595,1831,878],{},[599,1833,1834],{"encoding":601},"0{,}0998334\\ldots",[572,1836,1838],{"className":1837,"ariaHidden":607},[606],[572,1839,1841,1844,1847,1853,1857,1860],{"className":1840},[611],[572,1842],{"className":1843,"style":891},[615],[572,1845,637],{"className":1846},[653],[572,1848,1850],{"className":1849},[653],[572,1851,734],{"className":1852},[776],[572,1854,1856],{"className":1855},[653],"0998334",[572,1858],{"className":1859,"style":781},[780],[572,1861,878],{"className":1862},[934],[564,1864,1865,1904],{},[572,1866,1868,1886],{"className":1867},[575],[572,1869,1871],{"className":1870},[579],[581,1872,1873],{"xmlns":583},[585,1874,1875,1883],{},[588,1876,1877,1879,1881],{},[591,1878,593],{},[595,1880,597],{},[635,1882,863],{},[599,1884,1885],{"encoding":601},"\\sin 1",[572,1887,1889],{"className":1888,"ariaHidden":607},[606],[572,1890,1892,1895,1898,1901],{"className":1891},[611],[572,1893],{"className":1894,"style":616},[615],[572,1896,593],{"className":1897},[620],[572,1899],{"className":1900,"style":781},[780],[572,1902,863],{"className":1903},[653]," mit drei Gliedern:",[572,1906,1909],{"className":1907},[1908],"katex-display",[572,1910,1912,1966],{"className":1911},[575],[572,1913,1915],{"className":1914},[579],[581,1916,1918],{"xmlns":583,"display":1917},"block",[585,1919,1920,1963],{},[588,1921,1922,1924,1926,1928,1930,1932,1934,1940,1942,1949,1951,1958,1960],{},[591,1923,593],{},[595,1925,597],{},[635,1927,863],{},[595,1929,1100],{},[635,1931,863],{},[595,1933,744],{},[1176,1935,1936,1938],{},[635,1937,863],{},[635,1939,1188],{},[595,1941,1476],{},[1176,1943,1944,1946],{},[635,1945,863],{},[635,1947,1948],{},"120",[595,1950,1467],{},[1176,1952,1953,1956],{},[635,1954,1955],{},"101",[635,1957,1948],{},[595,1959,1100],{},[635,1961,1962],{},"0,8417",[599,1964,1965],{"encoding":601},"\\sin 1 \\approx 1 - \\frac{1}{6} + \\frac{1}{120} = \\frac{101}{120} \\approx 0{,}8417",[572,1967,1969,1993,2012,2094,2171,2248],{"className":1968,"ariaHidden":607},[606],[572,1970,1972,1975,1978,1981,1984,1987,1990],{"className":1971},[611],[572,1973],{"className":1974,"style":616},[615],[572,1976,593],{"className":1977},[620],[572,1979],{"className":1980,"style":781},[780],[572,1982,863],{"className":1983},[653],[572,1985],{"className":1986,"style":1127},[780],[572,1988,1100],{"className":1989},[1131],[572,1991],{"className":1992,"style":1127},[780],[572,1994,1996,2000,2003,2006,2009],{"className":1995},[611],[572,1997],{"className":1998,"style":1999},[615],"height:0.7278em;vertical-align:-0.0833em;",[572,2001,863],{"className":2002},[653],[572,2004],{"className":2005,"style":1232},[780],[572,2007,744],{"className":2008},[1236],[572,2010],{"className":2011,"style":1232},[780],[572,2013,2015,2019,2085,2088,2091],{"className":2014},[611],[572,2016],{"className":2017,"style":2018},[615],"height:2.0074em;vertical-align:-0.686em;",[572,2020,2022,2025,2082],{"className":2021},[653],[572,2023],{"className":2024},[1253,1254],[572,2026,2028],{"className":2027},[1176],[572,2029,2031,2073],{"className":2030},[1261,1262],[572,2032,2034,2070],{"className":2033},[1266],[572,2035,2038,2050,2058],{"className":2036,"style":2037},[1270],"height:1.3214em;",[572,2039,2041,2044],{"style":2040},"top:-2.314em;",[572,2042],{"className":2043,"style":1279},[1278],[572,2045,2047],{"className":2046},[653],[572,2048,1188],{"className":2049},[653],[572,2051,2052,2055],{"style":1295},[572,2053],{"className":2054,"style":1279},[1278],[572,2056],{"className":2057,"style":1303},[1302],[572,2059,2061,2064],{"style":2060},"top:-3.677em;",[572,2062],{"className":2063,"style":1279},[1278],[572,2065,2067],{"className":2066},[653],[572,2068,863],{"className":2069},[653],[572,2071,1355],{"className":2072},[1354],[572,2074,2076],{"className":2075},[1266],[572,2077,2080],{"className":2078,"style":2079},[1270],"height:0.686em;",[572,2081],{},[572,2083],{"className":2084},[1368,1254],[572,2086],{"className":2087,"style":1232},[780],[572,2089,1476],{"className":2090},[1236],[572,2092],{"className":2093,"style":1232},[780],[572,2095,2097,2100,2162,2165,2168],{"className":2096},[611],[572,2098],{"className":2099,"style":2018},[615],[572,2101,2103,2106,2159],{"className":2102},[653],[572,2104],{"className":2105},[1253,1254],[572,2107,2109],{"className":2108},[1176],[572,2110,2112,2151],{"className":2111},[1261,1262],[572,2113,2115,2148],{"className":2114},[1266],[572,2116,2118,2129,2137],{"className":2117,"style":2037},[1270],[572,2119,2120,2123],{"style":2040},[572,2121],{"className":2122,"style":1279},[1278],[572,2124,2126],{"className":2125},[653],[572,2127,1948],{"className":2128},[653],[572,2130,2131,2134],{"style":1295},[572,2132],{"className":2133,"style":1279},[1278],[572,2135],{"className":2136,"style":1303},[1302],[572,2138,2139,2142],{"style":2060},[572,2140],{"className":2141,"style":1279},[1278],[572,2143,2145],{"className":2144},[653],[572,2146,863],{"className":2147},[653],[572,2149,1355],{"className":2150},[1354],[572,2152,2154],{"className":2153},[1266],[572,2155,2157],{"className":2156,"style":2079},[1270],[572,2158],{},[572,2160],{"className":2161},[1368,1254],[572,2163],{"className":2164,"style":1127},[780],[572,2166,1467],{"className":2167},[1131],[572,2169],{"className":2170,"style":1127},[780],[572,2172,2174,2177,2239,2242,2245],{"className":2173},[611],[572,2175],{"className":2176,"style":2018},[615],[572,2178,2180,2183,2236],{"className":2179},[653],[572,2181],{"className":2182},[1253,1254],[572,2184,2186],{"className":2185},[1176],[572,2187,2189,2228],{"className":2188},[1261,1262],[572,2190,2192,2225],{"className":2191},[1266],[572,2193,2195,2206,2214],{"className":2194,"style":2037},[1270],[572,2196,2197,2200],{"style":2040},[572,2198],{"className":2199,"style":1279},[1278],[572,2201,2203],{"className":2202},[653],[572,2204,1948],{"className":2205},[653],[572,2207,2208,2211],{"style":1295},[572,2209],{"className":2210,"style":1279},[1278],[572,2212],{"className":2213,"style":1303},[1302],[572,2215,2216,2219],{"style":2060},[572,2217],{"className":2218,"style":1279},[1278],[572,2220,2222],{"className":2221},[653],[572,2223,1955],{"className":2224},[653],[572,2226,1355],{"className":2227},[1354],[572,2229,2231],{"className":2230},[1266],[572,2232,2234],{"className":2233,"style":2079},[1270],[572,2235],{},[572,2237],{"className":2238},[1368,1254],[572,2240],{"className":2241,"style":1127},[780],[572,2243,1100],{"className":2244},[1131],[572,2246],{"className":2247,"style":1127},[780],[572,2249,2251,2254,2257,2263],{"className":2250},[611],[572,2252],{"className":2253,"style":891},[615],[572,2255,637],{"className":2256},[653],[572,2258,2260],{"className":2259},[653],[572,2261,734],{"className":2262},[776],[572,2264,2266],{"className":2265},[653],"8417",[564,2268,2269,2270,2310,2311,2546],{},"Der genaue Wert ist etwa ",[572,2271,2273,2288],{"className":2272},[575],[572,2274,2276],{"className":2275},[579],[581,2277,2278],{"xmlns":583},[585,2279,2280,2285],{},[588,2281,2282],{},[635,2283,2284],{},"0,8415",[599,2286,2287],{"encoding":601},"0{,}8415",[572,2289,2291],{"className":2290,"ariaHidden":607},[606],[572,2292,2294,2297,2300,2306],{"className":2293},[611],[572,2295],{"className":2296,"style":891},[615],[572,2298,637],{"className":2299},[653],[572,2301,2303],{"className":2302},[653],[572,2304,734],{"className":2305},[776],[572,2307,2309],{"className":2308},[653],"8415",". Der Fehler liegt unter dem nächsten Glied ",[572,2312,2314,2353],{"className":2313},[575],[572,2315,2317],{"className":2316},[579],[581,2318,2319],{"xmlns":583},[585,2320,2321,2350],{},[588,2322,2323,2336,2338,2345,2347],{},[1176,2324,2325,2327],{},[635,2326,863],{},[588,2328,2329,2332],{},[635,2330,2331],{},"7",[595,2333,2335],{"stretchy":2334},"false","!",[595,2337,1467],{},[1176,2339,2340,2342],{},[635,2341,863],{},[635,2343,2344],{},"5040",[595,2346,1100],{},[635,2348,2349],{},"0,000198",[599,2351,2352],{"encoding":601},"\\frac{1}{7!} = \\frac{1}{5040} \\approx 0{,}000198",[572,2354,2356,2444,2527],{"className":2355,"ariaHidden":607},[606],[572,2357,2359,2363,2435,2438,2441],{"className":2358},[611],[572,2360],{"className":2361,"style":2362},[615],"height:1.1901em;vertical-align:-0.345em;",[572,2364,2366,2369,2432],{"className":2365},[653],[572,2367],{"className":2368},[1253,1254],[572,2370,2372],{"className":2371},[1176],[572,2373,2375,2424],{"className":2374},[1261,1262],[572,2376,2378,2421],{"className":2377},[1266],[572,2379,2382,2399,2407],{"className":2380,"style":2381},[1270],"height:0.8451em;",[572,2383,2384,2387],{"style":1274},[572,2385],{"className":2386,"style":1279},[1278],[572,2388,2390],{"className":2389},[1283,1284,1285,1286],[572,2391,2393,2396],{"className":2392},[653,1286],[572,2394,2331],{"className":2395},[653,1286],[572,2397,2335],{"className":2398},[1368,1286],[572,2400,2401,2404],{"style":1295},[572,2402],{"className":2403,"style":1279},[1278],[572,2405],{"className":2406,"style":1303},[1302],[572,2408,2409,2412],{"style":1306},[572,2410],{"className":2411,"style":1279},[1278],[572,2413,2415],{"className":2414},[1283,1284,1285,1286],[572,2416,2418],{"className":2417},[653,1286],[572,2419,863],{"className":2420},[653,1286],[572,2422,1355],{"className":2423},[1354],[572,2425,2427],{"className":2426},[1266],[572,2428,2430],{"className":2429,"style":1362},[1270],[572,2431],{},[572,2433],{"className":2434},[1368,1254],[572,2436],{"className":2437,"style":1127},[780],[572,2439,1467],{"className":2440},[1131],[572,2442],{"className":2443,"style":1127},[780],[572,2445,2447,2450,2518,2521,2524],{"className":2446},[611],[572,2448],{"className":2449,"style":2362},[615],[572,2451,2453,2456,2515],{"className":2452},[653],[572,2454],{"className":2455},[1253,1254],[572,2457,2459],{"className":2458},[1176],[572,2460,2462,2507],{"className":2461},[1261,1262],[572,2463,2465,2504],{"className":2464},[1266],[572,2466,2468,2482,2490],{"className":2467,"style":2381},[1270],[572,2469,2470,2473],{"style":1274},[572,2471],{"className":2472,"style":1279},[1278],[572,2474,2476],{"className":2475},[1283,1284,1285,1286],[572,2477,2479],{"className":2478},[653,1286],[572,2480,2344],{"className":2481},[653,1286],[572,2483,2484,2487],{"style":1295},[572,2485],{"className":2486,"style":1279},[1278],[572,2488],{"className":2489,"style":1303},[1302],[572,2491,2492,2495],{"style":1306},[572,2493],{"className":2494,"style":1279},[1278],[572,2496,2498],{"className":2497},[1283,1284,1285,1286],[572,2499,2501],{"className":2500},[653,1286],[572,2502,863],{"className":2503},[653,1286],[572,2505,1355],{"className":2506},[1354],[572,2508,2510],{"className":2509},[1266],[572,2511,2513],{"className":2512,"style":1362},[1270],[572,2514],{},[572,2516],{"className":2517},[1368,1254],[572,2519],{"className":2520,"style":1127},[780],[572,2522,1100],{"className":2523},[1131],[572,2525],{"className":2526,"style":1127},[780],[572,2528,2530,2533,2536,2542],{"className":2529},[611],[572,2531],{"className":2532,"style":891},[615],[572,2534,637],{"className":2535},[653],[572,2537,2539],{"className":2538},[653],[572,2540,734],{"className":2541},[776],[572,2543,2545],{"className":2544},[653],"000198",".",[559,2548,2550],{"id":2549},"typische-fehler","Typische Fehler",[1075,2552,2553,2811,2979],{},[1078,2554,2555,2556,2634,2635,2759,2760,2546],{},"Den Winkel in Grad einsetzen. ",[572,2557,2559,2586],{"className":2558},[575],[572,2560,2562],{"className":2561},[579],[581,2563,2564],{"xmlns":583},[585,2565,2566,2583],{},[588,2567,2568,2570,2572,2575,2578,2580],{},[591,2569,593],{},[595,2571,597],{},[635,2573,2574],{},"30",[591,2576,2577],{"mathvariant":993},"°",[595,2579,1467],{},[635,2581,2582],{},"0,5",[599,2584,2585],{"encoding":601},"\\sin 30° = 0{,}5",[572,2587,2589,2615],{"className":2588,"ariaHidden":607},[606],[572,2590,2592,2596,2599,2602,2606,2609,2612],{"className":2591},[611],[572,2593],{"className":2594,"style":2595},[615],"height:0.6944em;",[572,2597,593],{"className":2598},[620],[572,2600],{"className":2601,"style":781},[780],[572,2603,2605],{"className":2604},[653],"30°",[572,2607],{"className":2608,"style":1127},[780],[572,2610,1467],{"className":2611},[1131],[572,2613],{"className":2614,"style":1127},[780],[572,2616,2618,2621,2624,2630],{"className":2617},[611],[572,2619],{"className":2620,"style":891},[615],[572,2622,637],{"className":2623},[653],[572,2625,2627],{"className":2626},[653],[572,2628,734],{"className":2629},[776],[572,2631,2633],{"className":2632},[653],"5"," erhält man nur mit ",[572,2636,2638,2661],{"className":2637},[575],[572,2639,2641],{"className":2640},[579],[581,2642,2643],{"xmlns":583},[585,2644,2645,2658],{},[588,2646,2647,2649,2651],{},[591,2648,961],{},[595,2650,1467],{},[1176,2652,2653,2656],{},[591,2654,2655],{},"π",[635,2657,1188],{},[599,2659,2660],{"encoding":601},"x = \\frac{\\pi}{6}",[572,2662,2664,2682],{"className":2663,"ariaHidden":607},[606],[572,2665,2667,2670,2673,2676,2679],{"className":2666},[611],[572,2668],{"className":2669,"style":973},[615],[572,2671,961],{"className":2672},[653,977],[572,2674],{"className":2675,"style":1127},[780],[572,2677,1467],{"className":2678},[1131],[572,2680],{"className":2681,"style":1127},[780],[572,2683,2685,2689],{"className":2684},[611],[572,2686],{"className":2687,"style":2688},[615],"height:1.0404em;vertical-align:-0.345em;",[572,2690,2692,2695,2756],{"className":2691},[653],[572,2693],{"className":2694},[1253,1254],[572,2696,2698],{"className":2697},[1176],[572,2699,2701,2748],{"className":2700},[1261,1262],[572,2702,2704,2745],{"className":2703},[1266],[572,2705,2708,2722,2730],{"className":2706,"style":2707},[1270],"height:0.6954em;",[572,2709,2710,2713],{"style":1274},[572,2711],{"className":2712,"style":1279},[1278],[572,2714,2716],{"className":2715},[1283,1284,1285,1286],[572,2717,2719],{"className":2718},[653,1286],[572,2720,1188],{"className":2721},[653,1286],[572,2723,2724,2727],{"style":1295},[572,2725],{"className":2726,"style":1279},[1278],[572,2728],{"className":2729,"style":1303},[1302],[572,2731,2732,2735],{"style":1306},[572,2733],{"className":2734,"style":1279},[1278],[572,2736,2738],{"className":2737},[1283,1284,1285,1286],[572,2739,2741],{"className":2740},[653,1286],[572,2742,2655],{"className":2743,"style":2744},[653,977,1286],"margin-right:0.0359em;",[572,2746,1355],{"className":2747},[1354],[572,2749,2751],{"className":2750},[1266],[572,2752,2754],{"className":2753,"style":1362},[1270],[572,2755],{},[572,2757],{"className":2758},[1368,1254],", nicht mit ",[572,2761,2763,2781],{"className":2762},[575],[572,2764,2766],{"className":2765},[579],[581,2767,2768],{"xmlns":583},[585,2769,2770,2778],{},[588,2771,2772,2774,2776],{},[591,2773,961],{},[595,2775,1467],{},[635,2777,2574],{},[599,2779,2780],{"encoding":601},"x = 30",[572,2782,2784,2802],{"className":2783,"ariaHidden":607},[606],[572,2785,2787,2790,2793,2796,2799],{"className":2786},[611],[572,2788],{"className":2789,"style":973},[615],[572,2791,961],{"className":2792},[653,977],[572,2794],{"className":2795,"style":1127},[780],[572,2797,1467],{"className":2798},[1131],[572,2800],{"className":2801,"style":1127},[780],[572,2803,2805,2808],{"className":2804},[611],[572,2806],{"className":2807,"style":649},[615],[572,2809,2574],{"className":2810},[653],[1078,2812,2813,2814,2874,2875,2909,2910,2944,2945,2546],{},"Potenz und Fakultät nicht zusammenpassen lassen: Zu ",[572,2815,2817,2835],{"className":2816},[575],[572,2818,2820],{"className":2819},[579],[581,2821,2822],{"xmlns":583},[585,2823,2824,2832],{},[588,2825,2826],{},[1179,2827,2828,2830],{},[591,2829,961],{},[635,2831,2633],{},[599,2833,2834],{"encoding":601},"x^5",[572,2836,2838],{"className":2837,"ariaHidden":607},[606],[572,2839,2841,2845],{"className":2840},[611],[572,2842],{"className":2843,"style":2844},[615],"height:0.8141em;",[572,2846,2848,2851],{"className":2847},[653],[572,2849,961],{"className":2850},[653,977],[572,2852,2854],{"className":2853},[1325],[572,2855,2857],{"className":2856},[1261],[572,2858,2860],{"className":2859},[1266],[572,2861,2863],{"className":2862,"style":2844},[1270],[572,2864,2865,2868],{"style":1518},[572,2866],{"className":2867,"style":1522},[1278],[572,2869,2871],{"className":2870},[1283,1284,1285,1286],[572,2872,2633],{"className":2873},[653,1286]," gehört ",[572,2876,2878,2894],{"className":2877},[575],[572,2879,2881],{"className":2880},[579],[581,2882,2883],{"xmlns":583},[585,2884,2885,2891],{},[588,2886,2887,2889],{},[635,2888,2633],{},[595,2890,2335],{"stretchy":2334},[599,2892,2893],{"encoding":601},"5!",[572,2895,2897],{"className":2896,"ariaHidden":607},[606],[572,2898,2900,2903,2906],{"className":2899},[611],[572,2901],{"className":2902,"style":2595},[615],[572,2904,2633],{"className":2905},[653],[572,2907,2335],{"className":2908},[1368],", nicht ",[572,2911,2913,2929],{"className":2912},[575],[572,2914,2916],{"className":2915},[579],[581,2917,2918],{"xmlns":583},[585,2919,2920,2926],{},[588,2921,2922,2924],{},[635,2923,700],{},[595,2925,2335],{"stretchy":2334},[599,2927,2928],{"encoding":601},"4!",[572,2930,2932],{"className":2931,"ariaHidden":607},[606],[572,2933,2935,2938,2941],{"className":2934},[611],[572,2936],{"className":2937,"style":2595},[615],[572,2939,700],{"className":2940},[653],[572,2942,2335],{"className":2943},[1368]," oder ",[572,2946,2948,2964],{"className":2947},[575],[572,2949,2951],{"className":2950},[579],[581,2952,2953],{"xmlns":583},[585,2954,2955,2961],{},[588,2956,2957,2959],{},[635,2958,1188],{},[595,2960,2335],{"stretchy":2334},[599,2962,2963],{"encoding":601},"6!",[572,2965,2967],{"className":2966,"ariaHidden":607},[606],[572,2968,2970,2973,2976],{"className":2969},[611],[572,2971],{"className":2972,"style":2595},[615],[572,2974,1188],{"className":2975},[653],[572,2977,2335],{"className":2978},[1368],[1078,2980,2981,2982,2546],{},"Gerade Potenzen mitnehmen oder die Vorzeichen nicht abwechseln lassen. Die Reihe mit lauter Pluszeichen ist die Reihe von ",[572,2983,2985,3004],{"className":2984},[575],[572,2986,2988],{"className":2987},[579],[581,2989,2990],{"xmlns":583},[585,2991,2992,3001],{},[588,2993,2994,2997,2999],{},[591,2995,2996],{},"sinh",[595,2998,597],{},[591,3000,961],{},[599,3002,3003],{"encoding":601},"\\sinh x",[572,3005,3007],{"className":3006,"ariaHidden":607},[606],[572,3008,3010,3013,3016,3019],{"className":3009},[611],[572,3011],{"className":3012,"style":2595},[615],[572,3014,2996],{"className":3015},[620],[572,3017],{"className":3018,"style":781},[780],[572,3020,961],{"className":3021},[653,977],{"title":3023,"searchDepth":3024,"depth":3024,"links":3025},"",2,[3026,3027,3028],{"id":561,"depth":3024,"text":562},{"id":1592,"depth":3024,"text":1593},{"id":2549,"depth":3024,"text":2550},[3030,3033,3036,3039,3042,3045,3048,3051,3053],{"lhs":3031,"rhs":3032},"sum(map(0:10, f(n) = (-1)^n * x^(2*n + 1)\u002F(2*n + 1)!))","sin(x)",{"lhs":3034,"rhs":3035},"round(0.1 - 0.1^3\u002F6, 7)","0.0998333",{"lhs":3037,"rhs":3038},"round(sin(0.1), 7)","0.0998334",{"lhs":3040,"rhs":3041},"1 - 1\u002F6 + 1\u002F120","101\u002F120",{"lhs":3043,"rhs":3044},"round(101\u002F120, 4)","0.8417",{"lhs":3046,"rhs":3047},"round(sin(1), 4)","0.8415",{"lhs":3049,"rhs":3050},"round(1\u002F5040, 6)","0.000198",{"lhs":3052,"rhs":637},"round((sin(x + 1e-5) - sin(x - 1e-5))\u002F2e-5 - sum(map(0:10, f(n) = (-1)^n * x^(2*n)\u002F(2*n)!)), 6)",{"lhs":3054,"rhs":3055},"round(sin(30*pi\u002F180), 9)","0.5","x \\in \\mathbb{R} \\text{ im Bogenmaß}","\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>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x \\in \\mathbb{R}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">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:0.6889em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">im Bogenmaß\u003C\u002Fspan>",null,"md","sine-series","\\sin x = \\sum_{n=0}^{\\infty} (-1)^n \\frac{x^{2n+1}}{(2n+1)!} = x - \\frac{x^3}{3!} + \\frac{x^5}{5!} - \\frac{x^7}{7!} + \\cdots","\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>sin\u003C\u002Fmi>\u003Cmo>⁡\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmunderover>\u003Cmo>∑\u003C\u002Fmo>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmi mathvariant=\"normal\">∞\u003C\u002Fmi>\u003C\u002Fmunderover>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmfrac>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmrow>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\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>\u003Cmfrac>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>5\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmrow>\u003Cmn>5\u003C\u002Fmn>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>−\u003C\u002Fmo>\u003Cmfrac>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>7\u003C\u002Fmn>\u003C\u002Fmsup>\u003Cmrow>\u003Cmn>7\u003C\u002Fmn>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003Cmo>+\u003C\u002Fmo>\u003Cmo>⋯\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\sin x = \\sum_{n=0}^{\\infty} (-1)^n \\frac{x^{2n+1}}{(2n+1)!} = x - \\frac{x^3}{3!} + \\frac{x^5}{5!} - \\frac{x^7}{7!} + \\cdots\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:0.6679em;\">\u003C\u002Fspan>\u003Cspan class=\"mop\">sin\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\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 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style=\"height:3.05em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">∞\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.2671em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">−\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mclose\">\u003Cspan class=\"mclose\">)\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\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\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\">1\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\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">+\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\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:0.936em;\">\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:0.6667em;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\">3\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\">3\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:0.2222em;\">\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\">5\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 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