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577,1105,1106,1109],{"style":837},[577,1107],{"className":1108,"style":828},[827],[577,1110,1112,1115,1118,1121,1125,1129,1132,1135],{"className":1111},[621],[577,1113,598],{"className":1114,"style":623},[621,622],[577,1116,647],{"className":1117},[796],[577,1119,598],{"className":1120,"style":623},[621,622],[577,1122],{"className":1123,"style":1124},[671],"margin-right:0.2222em;",[577,1126,722],{"className":1127},[1128],"mbin",[577,1130],{"className":1131,"style":1124},[671],[577,1133,666],{"className":1134},[621],[577,1136,660],{"className":1137},[864],[577,1139,851],{"className":1140},[850],[577,1142,1144],{"className":1143},[815],[577,1145,1147],{"className":1146,"style":858},[819],[577,1148],{},[577,1150],{"className":1151},[864,1068],[577,1153,669],{"className":1154},[891],[577,1156],{"className":1157,"style":895},[671],[577,1159],{"className":1160,"style":899},[671],[577,1162,1164,1170,1215],{"className":1163},[621],[577,1165,1167],{"className":1166,"style":798},[796,797],[577,1168,647],{"className":1169},[802,803],[577,1171,1173],{"className":1172},[649],[577,1174,1176,1207],{"className":1175},[810,811],[577,1177,1179,1204],{"className":1178},[815],[577,1180,1182,1193],{"className":1181,"style":820},[819],[577,1183,1184,1187],{"style":823},[577,1185],{"className":1186,"style":828},[827],[577,1188,1190],{"className":1189},[621],[577,1191,743],{"className":1192},[621],[577,1194,1195,1198],{"style":837},[577,1196],{"className":1197,"style":828},[827],[577,1199,1201],{"className":1200},[621],[577,1202,598],{"className":1203,"style":623},[621,622],[577,1205,851],{"className":1206},[850],[577,1208,1210],{"className":1209},[815],[577,1211,1213],{"className":1212,"style":858},[819],[577,1214],{},[577,1216,1218],{"className":1217,"style":798},[864,797],[577,1219,660],{"className":1220},[802,803],[577,1222],{"className":1223,"style":871},[671],[577,1225,663],{"className":1226},[875],[577,1228],{"className":1229,"style":871},[671],[577,1231,1233,1237],{"className":1232},[612],[577,1234],{"className":1235,"style":1236},[616],"height:2.113em;vertical-align:-0.686em;",[577,1238,1240,1243,1338],{"className":1239},[621],[577,1241],{"className":1242},[796,1068],[577,1244,1246],{"className":1245},[649],[577,1247,1249,1330],{"className":1248},[810,811],[577,1250,1252,1327],{"className":1251},[815],[577,1253,1255,1266,1274],{"className":1254,"style":1081},[819],[577,1256,1257,1260],{"style":823},[577,1258],{"className":1259,"style":828},[827],[577,1261,1263],{"className":1262},[621],[577,1264,776],{"className":1265},[621],[577,1267,1268,1271],{"style":1095},[577,1269],{"className":1270,"style":828},[827],[577,1272],{"className":1273,"style":1103},[1102],[577,1275,1276,1279],{"style":837},[577,1277],{"className":1278,"style":828},[827],[577,1280,1282,1285,1288,1291,1294,1297,1300,1303,1306,1309,1312,1315,1318,1321,1324],{"className":1281},[621],[577,1283,598],{"className":1284,"style":623},[621,622],[577,1286,647],{"className":1287},[796],[577,1289,598],{"className":1290,"style":623},[621,622],[577,1292],{"className":1293,"style":1124},[671],[577,1295,722],{"className":1296},[1128],[577,1298],{"className":1299,"style":1124},[671],[577,1301,666],{"className":1302},[621],[577,1304,660],{"className":1305},[864],[577,1307,647],{"className":1308},[796],[577,1310,598],{"className":1311,"style":623},[621,622],[577,1313],{"className":1314,"style":1124},[671],[577,1316,722],{"className":1317},[1128],[577,1319],{"className":1320,"style":1124},[671],[577,1322,704],{"className":1323},[621],[577,1325,660],{"className":1326},[864],[577,1328,851],{"className":1329},[850],[577,1331,1333],{"className":1332},[815],[577,1334,1336],{"className":1335,"style":858},[819],[577,1337],{},[577,1339],{"className":1340},[864,1068],[1342,1343,1344,1595],"ul",{},[1345,1346,1347,1348,1455,1456,1535,1536,1564,1565,1594],"li",{},"Ist 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wird ab ",[577,1457,1459,1483],{"className":1458},[580],[577,1460,1462],{"className":1461},[584],[586,1463,1464],{"xmlns":588},[590,1465,1466,1480],{},[593,1467,1468,1471,1473,1475,1478],{},[596,1469,1470],{},"k",[645,1472,663],{},[596,1474,598],{},[645,1476,1477],{},"+",[655,1479,666],{},[600,1481,1482],{"encoding":602},"k = \\alpha + 1",[577,1484,1486,1506,1525],{"className":1485,"ariaHidden":608},[607],[577,1487,1489,1493,1497,1500,1503],{"className":1488},[612],[577,1490],{"className":1491,"style":1492},[616],"height:0.6944em;",[577,1494,1470],{"className":1495,"style":1496},[621,622],"margin-right:0.0315em;",[577,1498],{"className":1499,"style":871},[671],[577,1501,663],{"className":1502},[875],[577,1504],{"className":1505,"style":871},[671],[577,1507,1509,1513,1516,1519,1522],{"className":1508},[612],[577,1510],{"className":1511,"style":1512},[616],"height:0.6667em;vertical-align:-0.0833em;",[577,1514,598],{"className":1515,"style":623},[621,622],[577,1517],{"className":1518,"style":1124},[671],[577,1520,1477],{"className":1521},[1128],[577,1523],{"className":1524,"style":1124},[671],[577,1526,1528,1532],{"className":1527},[612],[577,1529],{"className":1530,"style":1531},[616],"height:0.6444em;",[577,1533,666],{"className":1534},[621]," jeder Koeffizient ",[577,1537,1539,1552],{"className":1538},[580],[577,1540,1542],{"className":1541},[584],[586,1543,1544],{"xmlns":588},[590,1545,1546,1550],{},[593,1547,1548],{},[655,1549,657],{},[600,1551,657],{"encoding":602},[577,1553,1555],{"className":1554,"ariaHidden":608},[607],[577,1556,1558,1561],{"className":1557},[612],[577,1559],{"className":1560,"style":1531},[616],[577,1562,657],{"className":1563},[621],". Die Reihe bricht ab, und es bleibt der binomische Lehrsatz. Dann gilt die Formel für alle ",[577,1566,1568,1582],{"className":1567},[580],[577,1569,1571],{"className":1570},[584],[586,1572,1573],{"xmlns":588},[590,1574,1575,1580],{},[593,1576,1577],{},[596,1578,1579],{},"x",[600,1581,1579],{"encoding":602},[577,1583,1585],{"className":1584,"ariaHidden":608},[607],[577,1586,1588,1591],{"className":1587},[612],[577,1589],{"className":1590,"style":617},[616],[577,1592,1579],{"className":1593},[621,622],".",[1345,1596,1597,1598,1626,1627,1691,1692,1720],{},"Sonst ist der Konvergenzradius ",[577,1599,1601,1614],{"className":1600},[580],[577,1602,1604],{"className":1603},[584],[586,1605,1606],{"xmlns":588},[590,1607,1608,1612],{},[593,1609,1610],{},[655,1611,666],{},[600,1613,666],{"encoding":602},[577,1615,1617],{"className":1616,"ariaHidden":608},[607],[577,1618,1620,1623],{"className":1619},[612],[577,1621],{"className":1622,"style":1531},[616],[577,1624,666],{"className":1625},[621],". Am Rand ",[577,1628,1630,1654],{"className":1629},[580],[577,1631,1633],{"className":1632},[584],[586,1634,1635],{"xmlns":588},[590,1636,1637,1651],{},[593,1638,1639,1643,1645,1647,1649],{},[596,1640,1642],{"mathvariant":1641},"normal","∣",[596,1644,1579],{},[596,1646,1642],{"mathvariant":1641},[645,1648,663],{},[655,1650,666],{},[600,1652,1653],{"encoding":602},"|x| = 1",[577,1655,1657,1682],{"className":1656,"ariaHidden":608},[607],[577,1658,1660,1664,1667,1670,1673,1676,1679],{"className":1659},[612],[577,1661],{"className":1662,"style":1663},[616],"height:1em;vertical-align:-0.25em;",[577,1665,1642],{"className":1666},[621],[577,1668,1579],{"className":1669},[621,622],[577,1671,1642],{"className":1672},[621],[577,1674],{"className":1675,"style":871},[671],[577,1677,663],{"className":1678},[875],[577,1680],{"className":1681,"style":871},[671],[577,1683,1685,1688],{"className":1684},[612],[577,1686],{"className":1687,"style":1531},[616],[577,1689,666],{"className":1690},[621]," hängt die Konvergenz von ",[577,1693,1695,1708],{"className":1694},[580],[577,1696,1698],{"className":1697},[584],[586,1699,1700],{"xmlns":588},[590,1701,1702,1706],{},[593,1703,1704],{},[596,1705,598],{},[600,1707,603],{"encoding":602},[577,1709,1711],{"className":1710,"ariaHidden":608},[607],[577,1712,1714,1717],{"className":1713},[612],[577,1715],{"className":1716,"style":617},[616],[577,1718,598],{"className":1719,"style":623},[621,622]," ab.",[564,1722,1723,1724,1727,1728,1873,1874,1594],{},"Die ersten beiden Glieder liefern die oft benutzte ",[568,1725,1726],{},"lineare Näherung"," ",[577,1729,1731,1769],{"className":1730},[580],[577,1732,1734],{"className":1733},[584],[586,1735,1736],{"xmlns":588},[590,1737,1738,1766],{},[593,1739,1740,1742,1744,1746,1748,1755,1758,1760,1762,1764],{},[645,1741,647],{"stretchy":717},[655,1743,666],{},[645,1745,1477],{},[596,1747,1579],{},[1749,1750,1751,1753],"msup",{},[645,1752,660],{"stretchy":717},[596,1754,598],{},[645,1756,1757],{},"≈",[655,1759,666],{},[645,1761,1477],{},[596,1763,598],{},[596,1765,1579],{},[600,1767,1768],{"encoding":602},"(1 + x)^\\alpha \\approx 1 + \\alpha x",[577,1770,1772,1793,1842,1861],{"className":1771,"ariaHidden":608},[607],[577,1773,1775,1778,1781,1784,1787,1790],{"className":1774},[612],[577,1776],{"className":1777,"style":1663},[616],[577,1779,647],{"className":1780},[796],[577,1782,666],{"className":1783},[621],[577,1785],{"className":1786,"style":1124},[671],[577,1788,1477],{"className":1789},[1128],[577,1791],{"className":1792,"style":1124},[671],[577,1794,1796,1799,1802,1833,1836,1839],{"className":1795},[612],[577,1797],{"className":1798,"style":1663},[616],[577,1800,1579],{"className":1801},[621,622],[577,1803,1805,1808],{"className":1804},[864],[577,1806,660],{"className":1807},[864],[577,1809,1811],{"className":1810},[1416],[577,1812,1814],{"className":1813},[810],[577,1815,1817],{"className":1816},[815],[577,1818,1821],{"className":1819,"style":1820},[819],"height:0.6644em;",[577,1822,1824,1827],{"style":1823},"top:-3.063em;margin-right:0.05em;",[577,1825],{"className":1826,"style":1433},[827],[577,1828,1830],{"className":1829},[1437,1438,803,1439],[577,1831,598],{"className":1832,"style":623},[621,622,1439],[577,1834],{"className":1835,"style":871},[671],[577,1837,1757],{"className":1838},[875],[577,1840],{"className":1841,"style":871},[671],[577,1843,1845,1849,1852,1855,1858],{"className":1844},[612],[577,1846],{"className":1847,"style":1848},[616],"height:0.7278em;vertical-align:-0.0833em;",[577,1850,666],{"className":1851},[621],[577,1853],{"className":1854,"style":1124},[671],[577,1856,1477],{"className":1857},[1128],[577,1859],{"className":1860,"style":1124},[671],[577,1862,1864,1867,1870],{"className":1863},[612],[577,1865],{"className":1866,"style":617},[616],[577,1868,598],{"className":1869,"style":623},[621,622],[577,1871,1579],{"className":1872},[621,622]," für kleine ",[577,1875,1877,1895],{"className":1876},[580],[577,1878,1880],{"className":1879},[584],[586,1881,1882],{"xmlns":588},[590,1883,1884,1892],{},[593,1885,1886,1888,1890],{},[596,1887,1642],{"mathvariant":1641},[596,1889,1579],{},[596,1891,1642],{"mathvariant":1641},[600,1893,1894],{"encoding":602},"|x|",[577,1896,1898],{"className":1897,"ariaHidden":608},[607],[577,1899,1901,1904,1907,1910],{"className":1900},[612],[577,1902],{"className":1903,"style":1663},[616],[577,1905,1642],{"className":1906},[621],[577,1908,1579],{"className":1909},[621,622],[577,1911,1642],{"className":1912},[621],[559,1914,1916],{"id":1915},"beispiele","Beispiele",[564,1918,1919,1920,2045,2046,2343],{},"Wurzel, 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\\cdots",[577,2415,2417,2509,2527,2605,2711,2814],{"className":2416,"ariaHidden":608},[607],[577,2418,2420,2424,2500,2503,2506],{"className":2419},[612],[577,2421],{"className":2422,"style":2423},[616],"height:1.04em;vertical-align:-0.1256em;",[577,2425,2428],{"className":2426},[621,2427],"sqrt",[577,2429,2431,2491],{"className":2430},[810,811],[577,2432,2434,2488],{"className":2433},[815],[577,2435,2438,2465],{"className":2436,"style":2437},[819],"height:0.9144em;",[577,2439,2443,2446],{"className":2440,"style":2442},[2441],"svg-align","top:-3em;",[577,2444],{"className":2445,"style":828},[827],[577,2447,2450,2453,2456,2459,2462],{"className":2448,"style":2449},[621],"padding-left:0.833em;",[577,2451,666],{"className":2452},[621],[577,2454],{"className":2455,"style":1124},[671],[577,2457,1477],{"className":2458},[1128],[577,2460],{"className":2461,"style":1124},[671],[577,2463,1579],{"className":2464},[621,622],[577,2466,2468,2471],{"style":2467},"top:-2.8744em;",[577,2469],{"className":2470,"style":828},[827],[577,2472,2476],{"className":2473,"style":2475},[2474],"hide-tail","min-width:0.853em;height:1.08em;",[2477,2478,2484],"svg",{"xmlns":2479,"width":2480,"height":2481,"viewBox":2482,"preserveAspectRatio":2483},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 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",[577,2828,2830,2849],{"className":2829},[580],[577,2831,2833],{"className":2832},[584],[586,2834,2835],{"xmlns":588},[590,2836,2837,2846],{},[593,2838,2839,2841,2843],{},[596,2840,1579],{},[645,2842,663],{},[655,2844,2845],{},"0,1",[600,2847,2848],{"encoding":602},"x = 0{,}1",[577,2850,2852,2870],{"className":2851,"ariaHidden":608},[607],[577,2853,2855,2858,2861,2864,2867],{"className":2854},[612],[577,2856],{"className":2857,"style":617},[616],[577,2859,1579],{"className":2860},[621,622],[577,2862],{"className":2863,"style":871},[671],[577,2865,663],{"className":2866},[875],[577,2868],{"className":2869,"style":871},[671],[577,2871,2873,2877,2880,2886],{"className":2872},[612],[577,2874],{"className":2875,"style":2876},[616],"height:0.8389em;vertical-align:-0.1944em;",[577,2878,657],{"className":2879},[621],[577,2881,2883],{"className":2882},[621],[577,2884,669],{"className":2885},[891],[577,2887,666],{"className":2888},[621],": ",[577,2891,2893,2934],{"className":2892},[580],[577,2894,2896],{"className":2895},[584],[586,2897,2898],{"xmlns":588},[590,2899,2900,2931],{},[593,2901,2902,2907,2909,2911,2913,2916,2918,2921,2923,2926,2928],{},[2360,2903,2904],{},[655,2905,2906],{},"1,1",[645,2908,1757],{},[655,2910,666],{},[645,2912,1477],{},[655,2914,2915],{},"0,05",[645,2917,722],{},[655,2919,2920],{},"0,00125",[645,2922,1477],{},[655,2924,2925],{},"0,0000625",[645,2927,663],{},[655,2929,2930],{},"1,0488125",[600,2932,2933],{"encoding":602},"\\sqrt{1{,}1} \\approx 1 + 0{,}05 - 0{,}00125 + 0{,}0000625 = 1{,}0488125",[577,2935,2937,3012,3030,3058,3086,3114],{"className":2936,"ariaHidden":608},[607],[577,2938,2940,2944,3003,3006,3009],{"className":2939},[612],[577,2941],{"className":2942,"style":2943},[616],"height:1.04em;vertical-align:-0.23em;",[577,2945,2947],{"className":2946},[621,2427],[577,2948,2950,2994],{"className":2949},[810,811],[577,2951,2953,2991],{"className":2952},[815],[577,2954,2957,2978],{"className":2955,"style":2956},[819],"height:0.81em;",[577,2958,2960,2963],{"className":2959,"style":2442},[2441],[577,2961],{"className":2962,"style":828},[827],[577,2964,2966,2969,2975],{"className":2965,"style":2449},[621],[577,2967,666],{"className":2968},[621],[577,2970,2972],{"className":2971},[621],[577,2973,669],{"className":2974},[891],[577,2976,666],{"className":2977},[621],[577,2979,2981,2984],{"style":2980},"top:-2.77em;",[577,2982],{"className":2983,"style":828},[827],[577,2985,2987],{"className":2986,"style":2475},[2474],[2477,2988,2989],{"xmlns":2479,"width":2480,"height":2481,"viewBox":2482,"preserveAspectRatio":2483},[2485,2990],{"d":2487},[577,2992,851],{"className":2993},[850],[577,2995,2997],{"className":2996},[815],[577,2998,3001],{"className":2999,"style":3000},[819],"height:0.23em;",[577,3002],{},[577,3004],{"className":3005,"style":871},[671],[577,3007,1757],{"className":3008},[875],[577,3010],{"className":3011,"style":871},[671],[577,3013,3015,3018,3021,3024,3027],{"className":3014},[612],[577,3016],{"className":3017,"style":1848},[616],[577,3019,666],{"className":3020},[621],[577,3022],{"className":3023,"style":1124},[671],[577,3025,1477],{"className":3026},[1128],[577,3028],{"className":3029,"style":1124},[671],[577,3031,3033,3036,3039,3045,3049,3052,3055],{"className":3032},[612],[577,3034],{"className":3035,"style":2876},[616],[577,3037,657],{"className":3038},[621],[577,3040,3042],{"className":3041},[621],[577,3043,669],{"className":3044},[891],[577,3046,3048],{"className":3047},[621],"05",[577,3050],{"className":3051,"style":1124},[671],[577,3053,722],{"className":3054},[1128],[577,3056],{"className":3057,"style":1124},[671],[577,3059,3061,3064,3067,3073,3077,3080,3083],{"className":3060},[612],[577,3062],{"className":3063,"style":2876},[616],[577,3065,657],{"className":3066},[621],[577,3068,3070],{"className":3069},[621],[577,3071,669],{"className":3072},[891],[577,3074,3076],{"className":3075},[621],"00125",[577,3078],{"className":3079,"style":1124},[671],[577,3081,1477],{"className":3082},[1128],[577,3084],{"className":3085,"style":1124},[671],[577,3087,3089,3092,3095,3101,3105,3108,3111],{"className":3088},[612],[577,3090],{"className":3091,"style":2876},[616],[577,3093,657],{"className":3094},[621],[577,3096,3098],{"className":3097},[621],[577,3099,669],{"className":3100},[891],[577,3102,3104],{"className":3103},[621],"0000625",[577,3106],{"className":3107,"style":871},[671],[577,3109,663],{"className":3110},[875],[577,3112],{"className":3113,"style":871},[671],[577,3115,3117,3120,3123,3129],{"className":3116},[612],[577,3118],{"className":3119,"style":2876},[616],[577,3121,666],{"className":3122},[621],[577,3124,3126],{"className":3125},[621],[577,3127,669],{"className":3128},[891],[577,3130,3132],{"className":3131},[621],"0488125",". Der genaue Wert ist ",[577,3135,3137,3154],{"className":3136},[580],[577,3138,3140],{"className":3139},[584],[586,3141,3142],{"xmlns":588},[590,3143,3144,3151],{},[593,3145,3146,3149],{},[655,3147,3148],{},"1,0488088",[645,3150,2092],{},[600,3152,3153],{"encoding":602},"1{,}0488088\\ldots",[577,3155,3157],{"className":3156,"ariaHidden":608},[607],[577,3158,3160,3163,3166,3172,3176,3179],{"className":3159},[612],[577,3161],{"className":3162,"style":2876},[616],[577,3164,666],{"className":3165},[621],[577,3167,3169],{"className":3168},[621],[577,3170,669],{"className":3171},[891],[577,3173,3175],{"className":3174},[621],"0488088",[577,3177],{"className":3178,"style":899},[671],[577,3180,2092],{"className":3181},[2342],[564,3183,3184,3240,3241,3317,3318],{},[577,3185,3187,3207],{"className":3186},[580],[577,3188,3190],{"className":3189},[584],[586,3191,3192],{"xmlns":588},[590,3193,3194,3204],{},[593,3195,3196,3198,3200,3202],{},[596,3197,598],{},[645,3199,663],{},[645,3201,722],{},[655,3203,666],{},[600,3205,3206],{"encoding":602},"\\alpha = -1",[577,3208,3210,3228],{"className":3209,"ariaHidden":608},[607],[577,3211,3213,3216,3219,3222,3225],{"className":3212},[612],[577,3214],{"className":3215,"style":617},[616],[577,3217,598],{"className":3218,"style":623},[621,622],[577,3220],{"className":3221,"style":871},[671],[577,3223,663],{"className":3224},[875],[577,3226],{"className":3227,"style":871},[671],[577,3229,3231,3234,3237],{"className":3230},[612],[577,3232],{"className":3233,"style":1848},[616],[577,3235,722],{"className":3236},[621],[577,3238,666],{"className":3239},[621],": Alle Koeffizienten sind ",[577,3242,3244,3268],{"className":3243},[580],[577,3245,3247],{"className":3246},[584],[586,3248,3249],{"xmlns":588},[590,3250,3251,3265],{},[593,3252,3253,3255,3257,3259],{},[645,3254,647],{"stretchy":717},[645,3256,722],{},[655,3258,666],{},[1749,3260,3261,3263],{},[645,3262,660],{"stretchy":717},[596,3264,1470],{},[600,3266,3267],{"encoding":602},"(-1)^k",[577,3269,3271],{"className":3270,"ariaHidden":608},[607],[577,3272,3274,3278,3281,3284,3287],{"className":3273},[612],[577,3275],{"className":3276,"style":3277},[616],"height:1.0991em;vertical-align:-0.25em;",[577,3279,647],{"className":3280},[796],[577,3282,722],{"className":3283},[621],[577,3285,666],{"className":3286},[621],[577,3288,3290,3293],{"className":3289},[864],[577,3291,660],{"className":3292},[864],[577,3294,3296],{"className":3295},[1416],[577,3297,3299],{"className":3298},[810],[577,3300,3302],{"className":3301},[815],[577,3303,3306],{"className":3304,"style":3305},[819],"height:0.8491em;",[577,3307,3308,3311],{"style":1823},[577,3309],{"className":3310,"style":1433},[827],[577,3312,3314],{"className":3313},[1437,1438,803,1439],[577,3315,1470],{"className":3316,"style":1496},[621,622,1439],", und es entsteht die geometrische Reihe ",[577,3319,3321,3373],{"className":3320},[580],[577,3322,3324],{"className":3323},[584],[586,3325,3326],{"xmlns":588},[590,3327,3328,3370],{},[593,3329,3330,3342,3344,3346,3348,3350,3352,3358,3360,3366,3368],{},[649,3331,3332,3334],{},[655,3333,666],{},[593,3335,3336,3338,3340],{},[655,3337,666],{},[645,3339,1477],{},[596,3341,1579],{},[645,3343,663],{},[655,3345,666],{},[645,3347,722],{},[596,3349,1579],{},[645,3351,1477],{},[1749,3353,3354,3356],{},[596,3355,1579],{},[655,3357,704],{},[645,3359,722],{},[1749,3361,3362,3364],{},[596,3363,1579],{},[655,3365,743],{},[645,3367,1477],{},[645,3369,2410],{},[600,3371,3372],{"encoding":602},"\\frac{1}{1 + x} = 1 - x + x^2 - x^3 + \\cdots",[577,3374,3376,3467,3485,3503,3548,3592],{"className":3375,"ariaHidden":608},[607],[577,3377,3379,3383,3458,3461,3464],{"className":3378},[612],[577,3380],{"className":3381,"style":3382},[616],"height:1.2484em;vertical-align:-0.4033em;",[577,3384,3386,3389,3455],{"className":3385},[621],[577,3387],{"className":3388},[796,1068],[577,3390,3392],{"className":3391},[649],[577,3393,3395,3446],{"className":3394},[810,811],[577,3396,3398,3443],{"className":3397},[815],[577,3399,3401,3421,3429],{"className":3400,"style":1991},[819],[577,3402,3403,3406],{"style":1994},[577,3404],{"className":3405,"style":828},[827],[577,3407,3409],{"className":3408},[1437,1438,803,1439],[577,3410,3412,3415,3418],{"className":3411},[621,1439],[577,3413,666],{"className":3414},[621,1439],[577,3416,1477],{"className":3417},[1128,1439],[577,3419,1579],{"className":3420},[621,622,1439],[577,3422,3423,3426],{"style":1095},[577,3424],{"className":3425,"style":828},[827],[577,3427],{"className":3428,"style":1103},[1102],[577,3430,3431,3434],{"style":2017},[577,3432],{"className":3433,"style":828},[827],[577,3435,3437],{"className":3436},[1437,1438,803,1439],[577,3438,3440],{"className":3439},[621,1439],[577,3441,666],{"className":3442},[621,1439],[577,3444,851],{"className":3445},[850],[577,3447,3449],{"className":3448},[815],[577,3450,3453],{"className":3451,"style":3452},[819],"height:0.4033em;",[577,3454],{},[577,3456],{"className":3457},[864,1068],[577,3459],{"className":3460,"style":871},[671],[577,3462,663],{"className":3463},[875],[577,3465],{"className":3466,"style":871},[671],[577,3468,3470,3473,3476,3479,3482],{"className":3469},[612],[577,3471],{"className":3472,"style":1848},[616],[577,3474,666],{"className":3475},[621],[577,3477],{"className":3478,"style":1124},[671],[577,3480,722],{"className":3481},[1128],[577,3483],{"className":3484,"style":1124},[671],[577,3486,3488,3491,3494,3497,3500],{"className":3487},[612],[577,3489],{"className":3490,"style":1512},[616],[577,3492,1579],{"className":3493},[621,622],[577,3495],{"className":3496,"style":1124},[671],[577,3498,1477],{"className":3499},[1128],[577,3501],{"className":3502,"style":1124},[671],[577,3504,3506,3510,3539,3542,3545],{"className":3505},[612],[577,3507],{"className":3508,"style":3509},[616],"height:0.8974em;vertical-align:-0.0833em;",[577,3511,3513,3516],{"className":3512},[621],[577,3514,1579],{"className":3515},[621,622],[577,3517,3519],{"className":3518},[1416],[577,3520,3522],{"className":3521},[810],[577,3523,3525],{"className":3524},[815],[577,3526,3528],{"className":3527,"style":2676},[819],[577,3529,3530,3533],{"style":1823},[577,3531],{"className":3532,"style":1433},[827],[577,3534,3536],{"className":3535},[1437,1438,803,1439],[577,3537,704],{"className":3538},[621,1439],[577,3540],{"className":3541,"style":1124},[671],[577,3543,722],{"className":3544},[1128],[577,3546],{"className":3547,"style":1124},[671],[577,3549,3551,3554,3583,3586,3589],{"className":3550},[612],[577,3552],{"className":3553,"style":3509},[616],[577,3555,3557,3560],{"className":3556},[621],[577,3558,1579],{"className":3559},[621,622],[577,3561,3563],{"className":3562},[1416],[577,3564,3566],{"className":3565},[810],[577,3567,3569],{"className":3568},[815],[577,3570,3572],{"className":3571,"style":2676},[819],[577,3573,3574,3577],{"style":1823},[577,3575],{"className":3576,"style":1433},[827],[577,3578,3580],{"className":3579},[1437,1438,803,1439],[577,3581,743],{"className":3582},[621,1439],[577,3584],{"className":3585,"style":1124},[671],[577,3587,1477],{"className":3588},[1128],[577,3590],{"className":3591,"style":1124},[671],[577,3593,3595,3598],{"className":3594},[612],[577,3596],{"className":3597,"style":2820},[616],[577,3599,2410],{"className":3600},[2342],[564,3602,3603,3604,3729,3730,2889,3927,4345,4346,4537,4538,4578,4579,1594],{},"Relativistischer Faktor, ",[577,3605,3607,3631],{"className":3606},[580],[577,3608,3610],{"className":3609},[584],[586,3611,3612],{"xmlns":588},[590,3613,3614,3628],{},[593,3615,3616,3618,3620,3622],{},[596,3617,598],{},[645,3619,663],{},[645,3621,722],{},[649,3623,3624,3626],{},[655,3625,666],{},[655,3627,704],{},[600,3629,3630],{"encoding":602},"\\alpha = -\\frac{1}{2}",[577,3632,3634,3652],{"className":3633,"ariaHidden":608},[607],[577,3635,3637,3640,3643,3646,3649],{"className":3636},[612],[577,3638],{"className":3639,"style":617},[616],[577,3641,598],{"className":3642,"style":623},[621,622],[577,3644],{"className":3645,"style":871},[671],[577,3647,663],{"className":3648},[875],[577,3650],{"className":3651,"style":871},[671],[577,3653,3655,3658,3661],{"className":3654},[612],[577,3656],{"className":3657,"style":1972},[616],[577,3659,722],{"className":3660},[621],[577,3662,3664,3667,3726],{"className":3663},[621],[577,3665],{"className":3666},[796,1068],[577,3668,3670],{"className":3669},[649],[577,3671,3673,3718],{"className":3672},[810,811],[577,3674,3676,3715],{"className":3675},[815],[577,3677,3679,3693,3701],{"className":3678,"style":1991},[819],[577,3680,3681,3684],{"style":1994},[577,3682],{"className":3683,"style":828},[827],[577,3685,3687],{"className":3686},[1437,1438,803,1439],[577,3688,3690],{"className":3689},[621,1439],[577,3691,704],{"className":3692},[621,1439],[577,3694,3695,3698],{"style":1095},[577,3696],{"className":3697,"style":828},[827],[577,3699],{"className":3700,"style":1103},[1102],[577,3702,3703,3706],{"style":2017},[577,3704],{"className":3705,"style":828},[827],[577,3707,3709],{"className":3708},[1437,1438,803,1439],[577,3710,3712],{"className":3711},[621,1439],[577,3713,666],{"className":3714},[621,1439],[577,3716,851],{"className":3717},[850],[577,3719,3721],{"className":3720},[815],[577,3722,3724],{"className":3723,"style":2039},[819],[577,3725],{},[577,3727],{"className":3728},[864,1068]," und ",[577,3731,3733,3767],{"className":3732},[580],[577,3734,3736],{"className":3735},[584],[586,3737,3738],{"xmlns":588},[590,3739,3740,3764],{},[593,3741,3742,3744,3746,3748],{},[596,3743,1579],{},[645,3745,663],{},[645,3747,722],{},[649,3749,3750,3757],{},[1749,3751,3752,3755],{},[596,3753,3754],{},"v",[655,3756,704],{},[1749,3758,3759,3762],{},[596,3760,3761],{},"c",[655,3763,704],{},[600,3765,3766],{"encoding":602},"x = -\\frac{v^2}{c^2}",[577,3768,3770,3788],{"className":3769,"ariaHidden":608},[607],[577,3771,3773,3776,3779,3782,3785],{"className":3772},[612],[577,3774],{"className":3775,"style":617},[616],[577,3777,1579],{"className":3778},[621,622],[577,3780],{"className":3781,"style":871},[671],[577,3783,663],{"className":3784},[875],[577,3786],{"className":3787,"style":871},[671],[577,3789,3791,3795,3798],{"className":3790},[612],[577,3792],{"className":3793,"style":3794},[616],"height:1.3629em;vertical-align:-0.345em;",[577,3796,722],{"className":3797},[621],[577,3799,3801,3804,3924],{"className":3800},[621],[577,3802],{"className":3803},[796,1068],[577,3805,3807],{"className":3806},[649],[577,3808,3810,3916],{"className":3809},[810,811],[577,3811,3813,3913],{"className":3812},[815],[577,3814,3817,3862,3870],{"className":3815,"style":3816},[819],"height:1.0179em;",[577,3818,3819,3822],{"style":1994},[577,3820],{"className":3821,"style":828},[827],[577,3823,3825],{"className":3824},[1437,1438,803,1439],[577,3826,3828],{"className":3827},[621,1439],[577,3829,3831,3834],{"className":3830},[621,1439],[577,3832,3761],{"className":3833},[621,622,1439],[577,3835,3837],{"className":3836},[1416],[577,3838,3840],{"className":3839},[810],[577,3841,3843],{"className":3842},[815],[577,3844,3847],{"className":3845,"style":3846},[819],"height:0.7463em;",[577,3848,3850,3854],{"style":3849},"top:-2.786em;margin-right:0.0714em;",[577,3851],{"className":3852,"style":3853},[827],"height:2.5em;",[577,3855,3859],{"className":3856},[1437,3857,3858,1439],"reset-size3","size1",[577,3860,704],{"className":3861},[621,1439],[577,3863,3864,3867],{"style":1095},[577,3865],{"className":3866,"style":828},[827],[577,3868],{"className":3869,"style":1103},[1102],[577,3871,3872,3875],{"style":2017},[577,3873],{"className":3874,"style":828},[827],[577,3876,3878],{"className":3877},[1437,1438,803,1439],[577,3879,3881],{"className":3880},[621,1439],[577,3882,3884,3888],{"className":3883},[621,1439],[577,3885,3754],{"className":3886,"style":3887},[621,622,1439],"margin-right:0.0359em;",[577,3889,3891],{"className":3890},[1416],[577,3892,3894],{"className":3893},[810],[577,3895,3897],{"className":3896},[815],[577,3898,3901],{"className":3899,"style":3900},[819],"height:0.8913em;",[577,3902,3904,3907],{"style":3903},"top:-2.931em;margin-right:0.0714em;",[577,3905],{"className":3906,"style":3853},[827],[577,3908,3910],{"className":3909},[1437,3857,3858,1439],[577,3911,704],{"className":3912},[621,1439],[577,3914,851],{"className":3915},[850],[577,3917,3919],{"className":3918},[815],[577,3920,3922],{"className":3921,"style":2039},[819],[577,3923],{},[577,3925],{"className":3926},[864,1068],[577,3928,3930,3993],{"className":3929},[580],[577,3931,3933],{"className":3932},[584],[586,3934,3935],{"xmlns":588},[590,3936,3937,3990],{},[593,3938,3939,3966,3968,3970,3972],{},[649,3940,3941,3943],{},[655,3942,666],{},[2360,3944,3945],{},[593,3946,3947,3949,3951,3957,3960],{},[655,3948,666],{},[645,3950,722],{},[1749,3952,3953,3955],{},[596,3954,3754],{},[655,3956,704],{},[596,3958,3959],{"mathvariant":1641},"\u002F",[1749,3961,3962,3964],{},[596,3963,3761],{},[655,3965,704],{},[645,3967,1757],{},[655,3969,666],{},[645,3971,1477],{},[649,3973,3974,3980],{},[1749,3975,3976,3978],{},[596,3977,3754],{},[655,3979,704],{},[593,3981,3982,3984],{},[655,3983,704],{},[1749,3985,3986,3988],{},[596,3987,3761],{},[655,3989,704],{},[600,3991,3992],{"encoding":602},"\\frac{1}{\\sqrt{1 - v^2\u002Fc^2}} \\approx 1 + 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Für ",[577,4347,4349,4380],{"className":4348},[580],[577,4350,4352],{"className":4351},[584],[586,4353,4354],{"xmlns":588},[590,4355,4356,4377],{},[593,4357,4358,4372,4374],{},[649,4359,4360,4366],{},[1749,4361,4362,4364],{},[596,4363,3754],{},[655,4365,704],{},[1749,4367,4368,4370],{},[596,4369,3761],{},[655,4371,704],{},[645,4373,663],{},[655,4375,4376],{},"0,01",[600,4378,4379],{"encoding":602},"\\frac{v^2}{c^2} = 0{,}01",[577,4381,4383,4518],{"className":4382,"ariaHidden":608},[607],[577,4384,4386,4389,4509,4512,4515],{"className":4385},[612],[577,4387],{"className":4388,"style":3794},[616],[577,4390,4392,4395,4506],{"className":4391},[621],[577,4393],{"className":4394},[796,1068],[577,4396,4398],{"className":4397},[649],[577,4399,4401,4498],{"className":4400},[810,811],[577,4402,4404,4495],{"className":4403},[815],[577,4405,4407,4447,4455],{"className":4406,"style":3816},[819],[577,4408,4409,4412],{"style":1994},[577,4410],{"className":4411,"style":828},[827],[577,4413,4415],{"className":4414},[1437,1438,803,1439],[577,4416,4418],{"className":4417},[621,1439],[577,4419,4421,4424],{"className":4420},[621,1439],[577,4422,3761],{"className":4423},[621,622,1439],[577,4425,4427],{"className":4426},[1416],[577,4428,4430],{"className":4429},[810],[577,4431,4433],{"className":4432},[815],[577,4434,4436],{"className":4435,"style":3846},[819],[577,4437,4438,4441],{"style":3849},[577,4439],{"className":4440,"style":3853},[827],[577,4442,4444],{"className":4443},[1437,3857,3858,1439],[577,4445,704],{"className":4446},[621,1439],[577,4448,4449,4452],{"style":1095},[577,4450],{"className":4451,"style":828},[827],[577,4453],{"className":4454,"style":1103},[1102],[577,4456,4457,4460],{"style":2017},[577,4458],{"className":4459,"style":828},[827],[577,4461,4463],{"className":4462},[1437,1438,803,1439],[577,4464,4466],{"className":4465},[621,1439],[577,4467,4469,4472],{"className":4468},[621,1439],[577,4470,3754],{"className":4471,"style":3887},[621,622,1439],[577,4473,4475],{"className":4474},[1416],[577,4476,4478],{"className":4477},[810],[577,4479,4481],{"className":4480},[815],[577,4482,4484],{"className":4483,"style":3900},[819],[577,4485,4486,4489],{"style":3903},[577,4487],{"className":4488,"style":3853},[827],[577,4490,4492],{"className":4491},[1437,3857,3858,1439],[577,4493,704],{"className":4494},[621,1439],[577,4496,851],{"className":4497},[850],[577,4499,4501],{"className":4500},[815],[577,4502,4504],{"className":4503,"style":2039},[819],[577,4505],{},[577,4507],{"className":4508},[864,1068],[577,4510],{"className":4511,"style":871},[671],[577,4513,663],{"className":4514},[875],[577,4516],{"className":4517,"style":871},[671],[577,4519,4521,4524,4527,4533],{"className":4520},[612],[577,4522],{"className":4523,"style":2876},[616],[577,4525,657],{"className":4526},[621],[577,4528,4530],{"className":4529},[621],[577,4531,669],{"className":4532},[891],[577,4534,4536],{"className":4535},[621],"01"," ergibt die Näherung ",[577,4539,4541,4556],{"className":4540},[580],[577,4542,4544],{"className":4543},[584],[586,4545,4546],{"xmlns":588},[590,4547,4548,4553],{},[593,4549,4550],{},[655,4551,4552],{},"1,005",[600,4554,4555],{"encoding":602},"1{,}005",[577,4557,4559],{"className":4558,"ariaHidden":608},[607],[577,4560,4562,4565,4568,4574],{"className":4561},[612],[577,4563],{"className":4564,"style":2876},[616],[577,4566,666],{"className":4567},[621],[577,4569,4571],{"className":4570},[621],[577,4572,669],{"className":4573},[891],[577,4575,4577],{"className":4576},[621],"005",", genau ist es ",[577,4580,4582,4597],{"className":4581},[580],[577,4583,4585],{"className":4584},[584],[586,4586,4587],{"xmlns":588},[590,4588,4589,4594],{},[593,4590,4591],{},[655,4592,4593],{},"1,005038",[600,4595,4596],{"encoding":602},"1{,}005038",[577,4598,4600],{"className":4599,"ariaHidden":608},[607],[577,4601,4603,4606,4609,4615],{"className":4602},[612],[577,4604],{"className":4605,"style":2876},[616],[577,4607,666],{"className":4608},[621],[577,4610,4612],{"className":4611},[621],[577,4613,669],{"className":4614},[891],[577,4616,4618],{"className":4617},[621],"005038",[559,4620,4622],{"id":4621},"typische-fehler","Typische Fehler",[1342,4624,4625,5363,5599],{},[1345,4626,4627,4628,4780,4781,4892,4893,5263,5264,5362],{},"Den Binomialkoeffizienten wie bei natürlichen Zahlen über ",[577,4629,4631,4674],{"className":4630},[580],[577,4632,4634],{"className":4633},[584],[586,4635,4636],{"xmlns":588},[590,4637,4638,4671],{},[593,4639,4640],{},[649,4641,4642,4649],{},[593,4643,4644,4646],{},[596,4645,598],{},[645,4647,4648],{"stretchy":717},"!",[593,4650,4651,4653,4655,4659,4661,4663,4665,4667,4669],{},[596,4652,1470],{},[645,4654,4648],{"stretchy":717},[4656,4657,4658],"mtext",{}," ",[645,4660,647],{"stretchy":717},[596,4662,598],{},[645,4664,722],{},[596,4666,1470],{},[645,4668,660],{"stretchy":717},[645,4670,4648],{"stretchy":717},[600,4672,4673],{"encoding":602},"\\frac{\\alpha!}{k!\\,(\\alpha - 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",[577,4782,4784,4812],{"className":4783},[580],[577,4785,4787],{"className":4786},[584],[586,4788,4789],{"xmlns":588},[590,4790,4791,4809],{},[593,4792,4793,4795,4807],{},[645,4794,647],{"fence":608},[649,4796,4797,4805],{"linethickness":651},[593,4798,4799,4801,4803],{},[655,4800,666],{},[596,4802,3959],{"mathvariant":1641},[655,4804,704],{},[655,4806,704],{},[645,4808,660],{"fence":608},[600,4810,4811],{"encoding":602},"\\binom{1\u002F2}{2}",[577,4813,4815],{"className":4814,"ariaHidden":608},[607],[577,4816,4818,4822],{"className":4817},[612],[577,4819],{"className":4820,"style":4821},[616],"height:1.319em;vertical-align:-0.35em;",[577,4823,4825,4831,4886],{"className":4824},[621],[577,4826,4828],{"className":4827,"style":798},[796,797],[577,4829,647],{"className":4830},[802,3858],[577,4832,4834],{"className":4833},[649],[577,4835,4837,4878],{"className":4836},[810,811],[577,4838,4840,4875],{"className":4839},[815],[577,4841,4844,4859],{"className":4842,"style":4843},[819],"height:0.969em;",[577,4845,4847,4850],{"style":4846},"top:-2.355em;",[577,4848],{"className":4849,"style":1433},[827],[577,4851,4853],{"className":4852},[1437,1438,803,1439],[577,4854,4856],{"className":4855},[621,1439],[577,4857,704],{"className":4858},[621,1439],[577,4860,4862,4865],{"style":4861},"top:-3.144em;",[577,4863],{"className":4864,"style":1433},[827],[577,4866,4868],{"className":4867},[1437,1438,803,1439],[577,4869,4871],{"className":4870},[621,1439],[577,4872,4874],{"className":4873},[621,1439],"1\u002F2",[577,4876,851],{"className":4877},[850],[577,4879,4881],{"className":4880},[815],[577,4882,4884],{"className":4883,"style":2039},[819],[577,4885],{},[577,4887,4889],{"className":4888,"style":798},[864,797],[577,4890,660],{"className":4891},[802,3858]," ist das Produkt ",[577,4894,4896,4945],{"className":4895},[580],[577,4897,4899],{"className":4898},[584],[586,4900,4901],{"xmlns":588},[590,4902,4903,4942],{},[593,4904,4905,4932,4934,4936],{},[649,4906,4907,4930],{},[593,4908,4909,4915,4918,4920,4922,4928],{},[649,4910,4911,4913],{},[655,4912,666],{},[655,4914,704],{},[645,4916,4917],{},"⋅",[645,4919,647],{"stretchy":717},[645,4921,722],{},[649,4923,4924,4926],{},[655,4925,666],{},[655,4927,704],{},[645,4929,660],{"stretchy":717},[655,4931,704],{},[645,4933,663],{},[645,4935,722],{},[649,4937,4938,4940],{},[655,4939,666],{},[655,4941,2078],{},[600,4943,4944],{"encoding":602},"\\frac{\\frac{1}{2} \\cdot (-\\frac{1}{2})}{2} = -\\frac{1}{8}",[577,4946,4948,5186],{"className":4947,"ariaHidden":608},[607],[577,4949,4951,4955,5177,5180,5183],{"className":4950},[612],[577,4952],{"className":4953,"style":4954},[616],"height:1.4868em;vertical-align:-0.345em;",[577,4956,4958,4961,5174],{"className":4957},[621],[577,4959],{"className":4960},[796,1068],[577,4962,4964],{"className":4963},[649],[577,4965,4967,5166],{"className":4966},[810,811],[577,4968,4970,5163],{"className":4969},[815],[577,4971,4974,4988,4996],{"className":4972,"style":4973},[819],"height:1.1418em;",[577,4975,4976,4979],{"style":1994},[577,4977],{"className":4978,"style":828},[827],[577,4980,4982],{"className":4981},[1437,1438,803,1439],[577,4983,4985],{"className":4984},[621,1439],[577,4986,704],{"className":4987},[621,1439],[577,4989,4990,4993],{"style":1095},[577,4991],{"className":4992,"style":828},[827],[577,4994],{"className":4995,"style":1103},[1102],[577,4997,4999,5002],{"style":4998},"top:-3.5508em;",[577,5000],{"className":5001,"style":828},[827],[577,5003,5005],{"className":5004},[1437,1438,803,1439],[577,5006,5008,5083,5086,5089,5092,5160],{"className":5007},[621,1439],[577,5009,5011,5015,5080],{"className":5010},[621,1439],[577,5012],{"className":5013},[796,1068,1437,3857,5014],"size6",[577,5016,5018],{"className":5017},[649],[577,5019,5021,5071],{"className":5020},[810,811],[577,5022,5024,5068],{"className":5023},[815],[577,5025,5028,5043,5053],{"className":5026,"style":5027},[819],"height:0.8443em;",[577,5029,5031,5034],{"style":5030},"top:-2.656em;",[577,5032],{"className":5033,"style":828},[827],[577,5035,5037],{"className":5036},[1437,3857,3858,1439],[577,5038,5040],{"className":5039},[621,1439],[577,5041,704],{"className":5042},[621,1439],[577,5044,5046,5049],{"style":5045},"top:-3.2255em;",[577,5047],{"className":5048,"style":828},[827],[577,5050],{"className":5051,"style":5052},[1102,1439],"border-bottom-width:0.049em;",[577,5054,5056,5059],{"style":5055},"top:-3.384em;",[577,5057],{"className":5058,"style":828},[827],[577,5060,5062],{"className":5061},[1437,3857,3858,1439],[577,5063,5065],{"className":5064},[621,1439],[577,5066,666],{"className":5067},[621,1439],[577,5069,851],{"className":5070},[850],[577,5072,5074],{"className":5073},[815],[577,5075,5078],{"className":5076,"style":5077},[819],"height:0.344em;",[577,5079],{},[577,5081],{"className":5082},[864,1068,1437,3857,5014],[577,5084,4917],{"className":5085},[1128,1439],[577,5087,647],{"className":5088},[796,1439],[577,5090,722],{"className":5091},[621,1439],[577,5093,5095,5098,5157],{"className":5094},[621,1439],[577,5096],{"className":5097},[796,1068,1437,3857,5014],[577,5099,5101],{"className":5100},[649],[577,5102,5104,5149],{"className":5103},[810,811],[577,5105,5107,5146],{"className":5106},[815],[577,5108,5110,5124,5132],{"className":5109,"style":5027},[819],[577,5111,5112,5115],{"style":5030},[577,5113],{"className":5114,"style":828},[827],[577,5116,5118],{"className":5117},[1437,3857,3858,1439],[577,5119,5121],{"className":5120},[621,1439],[577,5122,704],{"className":5123},[621,1439],[577,5125,5126,5129],{"style":5045},[577,5127],{"className":5128,"style":828},[827],[577,5130],{"className":5131,"style":5052},[1102,1439],[577,5133,5134,5137],{"style":5055},[577,5135],{"className":5136,"style":828},[827],[577,5138,5140],{"className":5139},[1437,3857,3858,1439],[577,5141,5143],{"className":5142},[621,1439],[577,5144,666],{"className":5145},[621,1439],[577,5147,851],{"className":5148},[850],[577,5150,5152],{"className":5151},[815],[577,5153,5155],{"className":5154,"style":5077},[819],[577,5156],{},[577,5158],{"className":5159},[864,1068,1437,3857,5014],[577,5161,660],{"className":5162},[864,1439],[577,5164,851],{"className":5165},[850],[577,5167,5169],{"className":5168},[815],[577,5170,5172],{"className":5171,"style":2039},[819],[577,5173],{},[577,5175],{"className":5176},[864,1068],[577,5178],{"className":5179,"style":871},[671],[577,5181,663],{"className":5182},[875],[577,5184],{"className":5185,"style":871},[671],[577,5187,5189,5192,5195],{"className":5188},[612],[577,5190],{"className":5191,"style":1972},[616],[577,5193,722],{"className":5194},[621],[577,5196,5198,5201,5260],{"className":5197},[621],[577,5199],{"className":5200},[796,1068],[577,5202,5204],{"className":5203},[649],[577,5205,5207,5252],{"className":5206},[810,811],[577,5208,5210,5249],{"className":5209},[815],[577,5211,5213,5227,5235],{"className":5212,"style":1991},[819],[577,5214,5215,5218],{"style":1994},[577,5216],{"className":5217,"style":828},[827],[577,5219,5221],{"className":5220},[1437,1438,803,1439],[577,5222,5224],{"className":5223},[621,1439],[577,5225,2078],{"className":5226},[621,1439],[577,5228,5229,5232],{"style":1095},[577,5230],{"className":5231,"style":828},[827],[577,5233],{"className":5234,"style":1103},[1102],[577,5236,5237,5240],{"style":2017},[577,5238],{"className":5239,"style":828},[827],[577,5241,5243],{"className":5242},[1437,1438,803,1439],[577,5244,5246],{"className":5245},[621,1439],[577,5247,666],{"className":5248},[621,1439],[577,5250,851],{"className":5251},[850],[577,5253,5255],{"className":5254},[815],[577,5256,5258],{"className":5257,"style":2039},[819],[577,5259],{},[577,5261],{"className":5262},[864,1068],", eine Fakultät von ",[577,5265,5267,5285],{"className":5266},[580],[577,5268,5270],{"className":5269},[584],[586,5271,5272],{"xmlns":588},[590,5273,5274,5282],{},[593,5275,5276],{},[649,5277,5278,5280],{},[655,5279,666],{},[655,5281,704],{},[600,5283,5284],{"encoding":602},"\\frac{1}{2}",[577,5286,5288],{"className":5287,"ariaHidden":608},[607],[577,5289,5291,5294],{"className":5290},[612],[577,5292],{"className":5293,"style":1972},[616],[577,5295,5297,5300,5359],{"className":5296},[621],[577,5298],{"className":5299},[796,1068],[577,5301,5303],{"className":5302},[649],[577,5304,5306,5351],{"className":5305},[810,811],[577,5307,5309,5348],{"className":5308},[815],[577,5310,5312,5326,5334],{"className":5311,"style":1991},[819],[577,5313,5314,5317],{"style":1994},[577,5315],{"className":5316,"style":828},[827],[577,5318,5320],{"className":5319},[1437,1438,803,1439],[577,5321,5323],{"className":5322},[621,1439],[577,5324,704],{"className":5325},[621,1439],[577,5327,5328,5331],{"style":1095},[577,5329],{"className":5330,"style":828},[827],[577,5332],{"className":5333,"style":1103},[1102],[577,5335,5336,5339],{"style":2017},[577,5337],{"className":5338,"style":828},[827],[577,5340,5342],{"className":5341},[1437,1438,803,1439],[577,5343,5345],{"className":5344},[621,1439],[577,5346,666],{"className":5347},[621,1439],[577,5349,851],{"className":5350},[850],[577,5352,5354],{"className":5353},[815],[577,5355,5357],{"className":5356,"style":2039},[819],[577,5358],{},[577,5360],{"className":5361},[864,1068]," kommt nicht vor.",[1345,5364,5365,5366,5428,5429,5598],{},"Die Reihe für ",[577,5367,5369,5392],{"className":5368},[580],[577,5370,5372],{"className":5371},[584],[586,5373,5374],{"xmlns":588},[590,5375,5376,5389],{},[593,5377,5378,5380,5382,5384,5387],{},[596,5379,1642],{"mathvariant":1641},[596,5381,1579],{},[596,5383,1642],{"mathvariant":1641},[645,5385,5386],{},"≥",[655,5388,666],{},[600,5390,5391],{"encoding":602},"|x| \\geq 1",[577,5393,5395,5419],{"className":5394,"ariaHidden":608},[607],[577,5396,5398,5401,5404,5407,5410,5413,5416],{"className":5397},[612],[577,5399],{"className":5400,"style":1663},[616],[577,5402,1642],{"className":5403},[621],[577,5405,1579],{"className":5406},[621,622],[577,5408,1642],{"className":5409},[621],[577,5411],{"className":5412,"style":871},[671],[577,5414,5386],{"className":5415},[875],[577,5417],{"className":5418,"style":871},[671],[577,5420,5422,5425],{"className":5421},[612],[577,5423],{"className":5424,"style":1531},[616],[577,5426,666],{"className":5427},[621]," verwenden. ",[577,5430,5432,5460],{"className":5431},[580],[577,5433,5435],{"className":5434},[584],[586,5436,5437],{"xmlns":588},[590,5438,5439,5457],{},[593,5440,5441,5445,5447],{},[2360,5442,5443],{},[655,5444,743],{},[645,5446,663],{},[2360,5448,5449],{},[593,5450,5451,5453,5455],{},[655,5452,666],{},[645,5454,1477],{},[655,5456,704],{},[600,5458,5459],{"encoding":602},"\\sqrt{3} = \\sqrt{1 + 2}",[577,5461,5463,5529],{"className":5462,"ariaHidden":608},[607],[577,5464,5466,5470,5520,5523,5526],{"className":5465},[612],[577,5467],{"className":5468,"style":5469},[616],"height:1.04em;vertical-align:-0.1328em;",[577,5471,5473],{"className":5472},[621,2427],[577,5474,5476,5511],{"className":5475},[810,811],[577,5477,5479,5508],{"className":5478},[815],[577,5480,5483,5495],{"className":5481,"style":5482},[819],"height:0.9072em;",[577,5484,5486,5489],{"className":5485,"style":2442},[2441],[577,5487],{"className":5488,"style":828},[827],[577,5490,5492],{"className":5491,"style":2449},[621],[577,5493,743],{"className":5494},[621],[577,5496,5498,5501],{"style":5497},"top:-2.8672em;",[577,5499],{"className":5500,"style":828},[827],[577,5502,5504],{"className":5503,"style":2475},[2474],[2477,5505,5506],{"xmlns":2479,"width":2480,"height":2481,"viewBox":2482,"preserveAspectRatio":2483},[2485,5507],{"d":2487},[577,5509,851],{"className":5510},[850],[577,5512,5514],{"className":5513},[815],[577,5515,5518],{"className":5516,"style":5517},[819],"height:0.1328em;",[577,5519],{},[577,5521],{"className":5522,"style":871},[671],[577,5524,663],{"className":5525},[875],[577,5527],{"className":5528,"style":871},[671],[577,5530,5532,5536],{"className":5531},[612],[577,5533],{"className":5534,"style":5535},[616],"height:1.04em;vertical-align:-0.1744em;",[577,5537,5539],{"className":5538},[621,2427],[577,5540,5542,5589],{"className":5541},[810,811],[577,5543,5545,5586],{"className":5544},[815],[577,5546,5549,5573],{"className":5547,"style":5548},[819],"height:0.8656em;",[577,5550,5552,5555],{"className":5551,"style":2442},[2441],[577,5553],{"className":5554,"style":828},[827],[577,5556,5558,5561,5564,5567,5570],{"className":5557,"style":2449},[621],[577,5559,666],{"className":5560},[621],[577,5562],{"className":5563,"style":1124},[671],[577,5565,1477],{"className":5566},[1128],[577,5568],{"className":5569,"style":1124},[671],[577,5571,704],{"className":5572},[621],[577,5574,5576,5579],{"style":5575},"top:-2.8256em;",[577,5577],{"className":5578,"style":828},[827],[577,5580,5582],{"className":5581,"style":2475},[2474],[2477,5583,5584],{"xmlns":2479,"width":2480,"height":2481,"viewBox":2482,"preserveAspectRatio":2483},[2485,5585],{"d":2487},[577,5587,851],{"className":5588},[850],[577,5590,5592],{"className":5591},[815],[577,5593,5596],{"className":5594,"style":5595},[819],"height:0.1744em;",[577,5597],{}," lässt sich so nicht berechnen.",[1345,5600,5601,5602,5721,5722,5821],{},"Die Vorzeichen falsch übernehmen. Bei 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werden die Faktoren ",[577,5723,5725,5755],{"className":5724},[580],[577,5726,5728],{"className":5727},[584],[586,5729,5730],{"xmlns":588},[590,5731,5732,5752],{},[593,5733,5734,5736,5738,5740,5742,5744,5746,5748,5750],{},[596,5735,598],{},[645,5737,722],{},[655,5739,666],{},[645,5741,669],{"separator":608},[596,5743,598],{},[645,5745,722],{},[655,5747,704],{},[645,5749,669],{"separator":608},[645,5751,2092],{},[600,5753,5754],{"encoding":602},"\\alpha - 1, \\alpha - 2, 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negativ, deshalb wechseln die Vorzeichen ab dem zweiten Glied.",{"title":5823,"searchDepth":5824,"depth":5824,"links":5825},"",2,[5826,5827,5828],{"id":561,"depth":5824,"text":562},{"id":1915,"depth":5824,"text":1916},{"id":4621,"depth":5824,"text":4622},[5830,5833,5836,5841,5845,5848,5851,5854,5859,5862,5865],{"lhs":5831,"rhs":5832},"(1\u002F2)*(1\u002F2 - 1)\u002F2!","-1\u002F8",{"lhs":5834,"rhs":5835},"(1\u002F2)*(1\u002F2 - 1)*(1\u002F2 - 2)\u002F3!","1\u002F16",{"lhs":5837,"rhs":5838,"where":5839},"1 + sum(map(1:40, f(k) = prod(map(1:k, g(j) = (a - j + 1)\u002Fj)) * x^k))","(1 + x)^a",{"x":5840},0.3,{"lhs":5842,"rhs":5838,"where":5843},"1 + sum(map(1:60, f(k) = prod(map(1:k, g(j) = (a - j + 1)\u002Fj)) * x^k))",{"x":5844},-0.5,{"lhs":5846,"rhs":5847},"1 + 0.1\u002F2 - 0.1^2\u002F8 + 0.1^3\u002F16","1.0488125",{"lhs":5849,"rhs":5850},"round(sqrt(1.1), 7)","1.0488088",{"lhs":5852,"rhs":5853},"(-1)*(-2)*(-3)\u002F3!","-1",{"lhs":5855,"rhs":5856,"where":5857},"round(sum(map(0:60, f(k) = (-x)^k)), 9)","round(1\u002F(1 + x), 9)",{"x":5858},0.4,{"lhs":5860,"rhs":5861},"round(1\u002Fsqrt(1 - 0.01), 6)","1.005038",{"lhs":5863,"rhs":5864},"1 + 0.01\u002F2","1.005",{"lhs":5866,"rhs":657},"3*2*1*0\u002F4!","\\alpha \\in \\mathbb{R},\\ |x| \u003C 1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>α\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\alpha \\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\" style=\"margin-right:0.0037em;\">α\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:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmo><\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">|x| < 1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\"><\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","binomial-series","(1 + x)^{\\alpha} = \\sum_{k=0}^{\\infty} \\binom{\\alpha}{k} x^k \\quad\\text{mit}\\quad \\binom{\\alpha}{k} = \\frac{\\alpha(\\alpha - 1)\\cdots(\\alpha - k + 1)}{k!}","\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>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmi>α\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>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmfrac linethickness=\"0px\">\u003Cmi>α\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmsup>\u003Cmi>x\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmspace width=\"1em\"\u002F>\u003Cmtext>mit\u003C\u002Fmtext>\u003Cmspace width=\"1em\"\u002F>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmfrac linethickness=\"0px\">\u003Cmi>α\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>α\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>α\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>⋯\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>α\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo stretchy=\"false\">!\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">(1 + x)^{\\alpha} = \\sum_{k=0}^{\\infty} \\binom{\\alpha}{k} x^k \\quad\\text{mit}\\quad \\binom{\\alpha}{k} = \\frac{\\alpha(\\alpha - 1)\\cdots(\\alpha - k + 1)}{k!}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\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 mtight\">\u003Cspan class=\"mord mathnormal mtight\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\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 delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1076em;\">\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\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 delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:0.8991em;\">\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\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:1em;\">\u003C\u002Fspan>\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\">mit\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:1em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1076em;\">\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\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 delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size3\">)\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:2.113em;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:1.427em;\">\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 mathnormal\" style=\"margin-right:0.0037em;\">α\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\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>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">⋯\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0037em;\">α\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 mathnormal\" style=\"margin-right:0.0315em;\">k\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>\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fbinomische-reihe",[],[5880,5881,5882,5883],"binomial-theorem","binomial-coefficient","taylor-series","geometric-series",{"title":548,"description":5823},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fbinomische-reihe","Für |x| \u003C 1 und beliebiges reelles α ist (1 + x)^α eine Potenzreihe mit verallgemeinerten Binomialkoeffizienten.",[5888,5889,5890,5891],"potenzreihe","binomialkoeffizient","näherung","wurzel",[5893,5896,5899,5902],{"symbol":1579,"meaning":5894,"symbolHtml":5895},"reelle Zahl mit |x| \u003C 1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath 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style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":5903,"meaning":5904,"symbolHtml":5905},"\\binom{\\alpha}{k}","verallgemeinerter Binomialkoeffizient, Produkt aus k Faktoren durch k!","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmfrac linethickness=\"0px\">\u003Cmi>α\u003C\u002Fmi>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\binom{\\alpha}{k}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.2em;vertical-align:-0.35em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen 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