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Davon gibt es ",[568,1072,1074,1093],{"className":1073},[571],[568,1075,1077],{"className":1076},[575],[577,1078,1079],{"xmlns":579},[581,1080,1081,1090],{},[584,1082,1083],{},[1084,1085,1086,1088],"mfrac",{},[587,1087,589],{},[649,1089,661],{},[591,1091,1092],{"encoding":593},"\\frac{n}{2}",[568,1094,1096],{"className":1095,"ariaHidden":598},[597],[568,1097,1099,1103],{"className":1098},[602],[568,1100],{"className":1101,"style":1102},[606],"height:1.0404em;vertical-align:-0.345em;",[568,1104,1106,1111,1178],{"className":1105},[611],[568,1107],{"className":1108},[1109,1110],"mopen","nulldelimiter",[568,1112,1114],{"className":1113},[1084],[568,1115,1117,1169],{"className":1116},[701,702],[568,1118,1120,1166],{"className":1119},[706],[568,1121,1124,1140,1151],{"className":1122,"style":1123},[710],"height:0.6954em;",[568,1125,1127,1131],{"style":1126},"top:-2.655em;",[568,1128],{"className":1129,"style":1130},[718],"height:3em;",[568,1132,1134],{"className":1133},[723,724,725,726],[568,1135,1137],{"className":1136},[611,726],[568,1138,661],{"className":1139},[611,726],[568,1141,1143,1146],{"style":1142},"top:-3.23em;",[568,1144],{"className":1145,"style":1130},[718],[568,1147],{"className":1148,"style":1150},[1149],"frac-line","border-bottom-width:0.04em;",[568,1152,1154,1157],{"style":1153},"top:-3.394em;",[568,1155],{"className":1156,"style":1130},[718],[568,1158,1160],{"className":1159},[723,724,725,726],[568,1161,1163],{"className":1162},[611,726],[568,1164,589],{"className":1165},[611,612,726],[568,1167,734],{"className":1168},[733],[568,1170,1172],{"className":1171},[706],[568,1173,1176],{"className":1174,"style":1175},[710],"height:0.345em;",[568,1177],{},[568,1179],{"className":1180},[1181,1110],"mclose"," Paare.",[564,1184,1185,1186,1189],{},"Man kann sich die Formel auch so merken: Anzahl der Glieder mal ",[615,1187,1188],{},"Mittelwert"," aus erstem und letztem Glied.",[564,1191,1192,1193,1410],{},"Die zweite Form entsteht, wenn man ",[568,1194,1196,1244],{"className":1195},[571],[568,1197,1199],{"className":1198},[575],[577,1200,1201],{"xmlns":579},[581,1202,1203,1241],{},[584,1204,1205,1211,1213,1219,1221,1225,1227,1230,1232,1235,1238],{},[632,1206,1207,1209],{},[587,1208,647],{},[587,1210,589],{},[640,1212,642],{},[632,1214,1215,1217],{},[587,1216,647],{},[649,1218,651],{},[640,1220,654],{},[640,1222,1224],{"stretchy":1223},"false","(",[587,1226,589],{},[640,1228,1229],{},"−",[649,1231,651],{},[640,1233,1234],{"stretchy":1223},")",[640,1236,1237],{},"⋅",[587,1239,1240],{},"d",[591,1242,1243],{"encoding":593},"a_n = a_1 + (n - 1) \\cdot d",[568,1245,1247,1302,1357,1379,1400],{"className":1246,"ariaHidden":598},[597],[568,1248,1250,1253,1293,1296,1299],{"className":1249},[602],[568,1251],{"className":1252,"style":687},[606],[568,1254,1256,1259],{"className":1255},[611],[568,1257,647],{"className":1258},[611,612],[568,1260,1262],{"className":1261},[697],[568,1263,1265,1285],{"className":1264},[701,702],[568,1266,1268,1282],{"className":1267},[706],[568,1269,1271],{"className":1270,"style":711},[710],[568,1272,1273,1276],{"style":714},[568,1274],{"className":1275,"style":719},[718],[568,1277,1279],{"className":1278},[723,724,725,726],[568,1280,589],{"className":1281},[611,612,726],[568,1283,734],{"className":1284},[733],[568,1286,1288],{"className":1287},[706],[568,1289,1291],{"className":1290,"style":741},[710],[568,1292],{},[568,1294],{"className":1295,"style":748},[747],[568,1297,642],{"className":1298},[752],[568,1300],{"className":1301,"style":748},[747],[568,1303,1305,1308,1348,1351,1354],{"className":1304},[602],[568,1306],{"className":1307,"style":762},[606],[568,1309,1311,1314],{"className":1310},[611],[568,1312,647],{"className":1313},[611,612],[568,1315,1317],{"className":1316},[697],[568,1318,1320,1340],{"className":1319},[701,702],[568,1321,1323,1337],{"className":1322},[706],[568,1324,1326],{"className":1325,"style":781},[710],[568,1327,1328,1331],{"style":714},[568,1329],{"className":1330,"style":719},[718],[568,1332,1334],{"className":1333},[723,724,725,726],[568,1335,651],{"className":1336},[611,726],[568,1338,734],{"className":1339},[733],[568,1341,1343],{"className":1342},[706],[568,1344,1346],{"className":1345,"style":741},[710],[568,1347],{},[568,1349],{"className":1350,"style":807},[747],[568,1352,654],{"className":1353},[811],[568,1355],{"className":1356,"style":807},[747],[568,1358,1360,1364,1367,1370,1373,1376],{"className":1359},[602],[568,1361],{"className":1362,"style":1363},[606],"height:1em;vertical-align:-0.25em;",[568,1365,1224],{"className":1366},[1109],[568,1368,589],{"className":1369},[611,612],[568,1371],{"className":1372,"style":807},[747],[568,1374,1229],{"className":1375},[811],[568,1377],{"className":1378,"style":807},[747],[568,1380,1382,1385,1388,1391,1394,1397],{"className":1381},[602],[568,1383],{"className":1384,"style":1363},[606],[568,1386,651],{"className":1387},[611],[568,1389,1234],{"className":1390},[1181],[568,1392],{"className":1393,"style":807},[747],[568,1395,1237],{"className":1396},[811],[568,1398],{"className":1399,"style":807},[747],[568,1401,1403,1407],{"className":1402},[602],[568,1404],{"className":1405,"style":1406},[606],"height:0.6944em;",[568,1408,1240],{"className":1409},[611,612]," einsetzt. Sie ist praktisch, wenn das letzte Glied nicht bekannt ist.",[559,1412,1414],{"id":1413},"herleitung","Herleitung",[564,1416,1417],{},"Man schreibt die Summe einmal vorwärts und einmal rückwärts untereinander:",[568,1419,1422],{"className":1420},[1421],"katex-display",[568,1423,1425,1548],{"className":1424},[571],[568,1426,1428],{"className":1427},[575],[577,1429,1431],{"xmlns":579,"display":1430},"block",[581,1432,1433,1545],{},[1434,1435,1439,1491],"mtable",{"rowspacing":1436,"columnalign":1437,"columnspacing":1438},"0.25em","right left","0em",[1440,1441,1442,1455],"mtr",{},[1443,1444,1445],"mtd",{},[1446,1447,1449],"mstyle",{"scriptlevel":1448,"displaystyle":598},"0",[632,1450,1451,1453],{},[587,1452,636],{},[587,1454,589],{},[1443,1456,1457],{},[1446,1458,1459],{"scriptlevel":1448,"displaystyle":598},[584,1460,1461,1463,1465,1471,1473,1479,1481,1483,1485],{},[584,1462],{},[640,1464,642],{},[632,1466,1467,1469],{},[587,1468,647],{},[649,1470,651],{},[640,1472,654],{},[632,1474,1475,1477],{},[587,1476,647],{},[649,1478,661],{},[640,1480,654],{},[640,1482,666],{},[640,1484,654],{},[632,1486,1487,1489],{},[587,1488,647],{},[587,1490,589],{},[1440,1492,1493,1503],{},[1443,1494,1495],{},[1446,1496,1497],{"scriptlevel":1448,"displaystyle":598},[632,1498,1499,1501],{},[587,1500,636],{},[587,1502,589],{},[1443,1504,1505],{},[1446,1506,1507],{"scriptlevel":1448,"displaystyle":598},[584,1508,1509,1511,1513,1519,1521,1533,1535,1537,1539],{},[584,1510],{},[640,1512,642],{},[632,1514,1515,1517],{},[587,1516,647],{},[587,1518,589],{},[640,1520,654],{},[632,1522,1523,1525],{},[587,1524,647],{},[584,1526,1527,1529,1531],{},[587,1528,589],{},[640,1530,1229],{},[649,1532,651],{},[640,1534,654],{},[640,1536,666],{},[640,1538,654],{},[632,1540,1541,1543],{},[587,1542,647],{},[649,1544,651],{},[591,1546,1547],{"encoding":593},"\\begin{aligned}\ns_n &= a_1 + a_2 + \\ldots + a_n \\\\\ns_n &= a_n + a_{n-1} + \\ldots + a_1\n\\end{aligned}",[568,1549,1551],{"className":1550,"ariaHidden":598},[597],[568,1552,1554,1558],{"className":1553},[602],[568,1555],{"className":1556,"style":1557},[606],"height:2.7em;vertical-align:-1.1em;",[568,1559,1561],{"className":1560},[611],[568,1562,1564,1688],{"className":1563},[1434],[568,1565,1568],{"className":1566},[1567],"col-align-r",[568,1569,1571,1679],{"className":1570},[701,702],[568,1572,1574,1676],{"className":1573},[706],[568,1575,1578,1627],{"className":1576,"style":1577},[710],"height:1.6em;",[568,1579,1581,1584],{"style":1580},"top:-3.76em;",[568,1582],{"className":1583,"style":1130},[718],[568,1585,1587],{"className":1586},[611],[568,1588,1590,1593],{"className":1589},[611],[568,1591,636],{"className":1592},[611,612],[568,1594,1596],{"className":1595},[697],[568,1597,1599,1619],{"className":1598},[701,702],[568,1600,1602,1616],{"className":1601},[706],[568,1603,1605],{"className":1604,"style":711},[710],[568,1606,1607,1610],{"style":714},[568,1608],{"className":1609,"style":719},[718],[568,1611,1613],{"className":1612},[723,724,725,726],[568,1614,589],{"className":1615},[611,612,726],[568,1617,734],{"className":1618},[733],[568,1620,1622],{"className":1621},[706],[568,1623,1625],{"className":1624,"style":741},[710],[568,1626],{},[568,1628,1630,1633],{"style":1629},"top:-2.26em;",[568,1631],{"className":1632,"style":1130},[718],[568,1634,1636],{"className":1635},[611],[568,1637,1639,1642],{"className":1638},[611],[568,1640,636],{"className":1641},[611,612],[568,1643,1645],{"className":1644},[697],[568,1646,1648,1668],{"className":1647},[701,702],[568,1649,1651,1665],{"className":1650},[706],[568,1652,1654],{"className":1653,"style":711},[710],[568,1655,1656,1659],{"style":714},[568,1657],{"className":1658,"style":719},[718],[568,1660,1662],{"className":1661},[723,724,725,726],[568,1663,589],{"className":1664},[611,612,726],[568,1666,734],{"className":1667},[733],[568,1669,1671],{"className":1670},[706],[568,1672,1674],{"className":1673,"style":741},[710],[568,1675],{},[568,1677,734],{"className":1678},[733],[568,1680,1682],{"className":1681},[706],[568,1683,1686],{"className":1684,"style":1685},[710],"height:1.1em;",[568,1687],{},[568,1689,1692],{"className":1690},[1691],"col-align-l",[568,1693,1695,2054],{"className":1694},[701,702],[568,1696,1698,2051],{"className":1697},[706],[568,1699,1701,1871],{"className":1700,"style":1577},[710],[568,1702,1703,1706],{"style":1580},[568,1704],{"className":1705,"style":1130},[718],[568,1707,1709,1712,1715,1718,1721,1761,1764,1767,1770,1810,1813,1816,1819,1822,1825,1828,1831],{"className":1708},[611],[568,1710],{"className":1711},[611],[568,1713],{"className":1714,"style":748},[747],[568,1716,642],{"className":1717},[752],[568,1719],{"className":1720,"style":748},[747],[568,1722,1724,1727],{"className":1723},[611],[568,1725,647],{"className":1726},[611,612],[568,1728,1730],{"className":1729},[697],[568,1731,1733,1753],{"className":1732},[701,702],[568,1734,1736,1750],{"className":1735},[706],[568,1737,1739],{"className":1738,"style":781},[710],[568,1740,1741,1744],{"style":714},[568,1742],{"className":1743,"style":719},[718],[568,1745,1747],{"className":1746},[723,724,725,726],[568,1748,651],{"className":1749},[611,726],[568,1751,734],{"className":1752},[733],[568,1754,1756],{"className":1755},[706],[568,1757,1759],{"className":1758,"style":741},[710],[568,1760],{},[568,1762],{"className":1763,"style":807},[747],[568,1765,654],{"className":1766},[811],[568,1768],{"className":1769,"style":807},[747],[568,1771,1773,1776],{"className":1772},[611],[568,1774,647],{"className":1775},[611,612],[568,1777,1779],{"className":1778},[697],[568,1780,1782,1802],{"className":1781},[701,702],[568,1783,1785,1799],{"className":1784},[706],[568,1786,1788],{"className":1787,"style":781},[710],[568,1789,1790,1793],{"style":714},[568,1791],{"className":1792,"style":719},[718],[568,1794,1796],{"className":1795},[723,724,725,726],[568,1797,661],{"className":1798},[611,726],[568,1800,734],{"className":1801},[733],[568,1803,1805],{"className":1804},[706],[568,1806,1808],{"className":1807,"style":741},[710],[568,1809],{},[568,1811],{"className":1812,"style":807},[747],[568,1814,654],{"className":1815},[811],[568,1817],{"className":1818,"style":807},[747],[568,1820,666],{"className":1821},[880],[568,1823],{"className":1824,"style":807},[747],[568,1826,654],{"className":1827},[811],[568,1829],{"className":1830,"style":807},[747],[568,1832,1834,1837],{"className":1833},[611],[568,1835,647],{"className":1836},[611,612],[568,1838,1840],{"className":1839},[697],[568,1841,1843,1863],{"className":1842},[701,702],[568,1844,1846,1860],{"className":1845},[706],[568,1847,1849],{"className":1848,"style":711},[710],[568,1850,1851,1854],{"style":714},[568,1852],{"className":1853,"style":719},[718],[568,1855,1857],{"className":1856},[723,724,725,726],[568,1858,589],{"className":1859},[611,612,726],[568,1861,734],{"className":1862},[733],[568,1864,1866],{"className":1865},[706],[568,1867,1869],{"className":1868,"style":741},[710],[568,1870],{},[568,1872,1873,1876],{"style":1629},[568,1874],{"className":1875,"style":1130},[718],[568,1877,1879,1882,1885,1888,1891,1931,1934,1937,1940,1990,1993,1996,1999,2002,2005,2008,2011],{"className":1878},[611],[568,1880],{"className":1881},[611],[568,1883],{"className":1884,"style":748},[747],[568,1886,642],{"className":1887},[752],[568,1889],{"className":1890,"style":748},[747],[568,1892,1894,1897],{"className":1893},[611],[568,1895,647],{"className":1896},[611,612],[568,1898,1900],{"className":1899},[697],[568,1901,1903,1923],{"className":1902},[701,702],[568,1904,1906,1920],{"className":1905},[706],[568,1907,1909],{"className":1908,"style":711},[710],[568,1910,1911,1914],{"style":714},[568,1912],{"className":1913,"style":719},[718],[568,1915,1917],{"className":1916},[723,724,725,726],[568,1918,589],{"className":1919},[611,612,726],[568,1921,734],{"className":1922},[733],[568,1924,1926],{"className":1925},[706],[568,1927,1929],{"className":1928,"style":741},[710],[568,1930],{},[568,1932],{"className":1933,"style":807},[747],[568,1935,654],{"className":1936},[811],[568,1938],{"className":1939,"style":807},[747],[568,1941,1943,1946],{"className":1942},[611],[568,1944,647],{"className":1945},[611,612],[568,1947,1949],{"className":1948},[697],[568,1950,1952,1981],{"className":1951},[701,702],[568,1953,1955,1978],{"className":1954},[706],[568,1956,1958],{"className":1957,"style":781},[710],[568,1959,1960,1963],{"style":714},[568,1961],{"className":1962,"style":719},[718],[568,1964,1966],{"className":1965},[723,724,725,726],[568,1967,1969,1972,1975],{"className":1968},[611,726],[568,1970,589],{"className":1971},[611,612,726],[568,1973,1229],{"className":1974},[811,726],[568,1976,651],{"className":1977},[611,726],[568,1979,734],{"className":1980},[733],[568,1982,1984],{"className":1983},[706],[568,1985,1988],{"className":1986,"style":1987},[710],"height:0.2083em;",[568,1989],{},[568,1991],{"className":1992,"style":807},[747],[568,1994,654],{"className":1995},[811],[568,1997],{"className":1998,"style":807},[747],[568,2000,666],{"className":2001},[880],[568,2003],{"className":2004,"style":807},[747],[568,2006,654],{"className":2007},[811],[568,2009],{"className":2010,"style":807},[747],[568,2012,2014,2017],{"className":2013},[611],[568,2015,647],{"className":2016},[611,612],[568,2018,2020],{"className":2019},[697],[568,2021,2023,2043],{"className":2022},[701,702],[568,2024,2026,2040],{"className":2025},[706],[568,2027,2029],{"className":2028,"style":781},[710],[568,2030,2031,2034],{"style":714},[568,2032],{"className":2033,"style":719},[718],[568,2035,2037],{"className":2036},[723,724,725,726],[568,2038,651],{"className":2039},[611,726],[568,2041,734],{"className":2042},[733],[568,2044,2046],{"className":2045},[706],[568,2047,2049],{"className":2048,"style":741},[710],[568,2050],{},[568,2052,734],{"className":2053},[733],[568,2055,2057],{"className":2056},[706],[568,2058,2060],{"className":2059,"style":1685},[710],[568,2061],{},[564,2063,2064,2065,2197,2198,2226,2227,2255,2256,2284,2285,2520],{},"Jede Spalte ergibt ",[568,2066,2068,2093],{"className":2067},[571],[568,2069,2071],{"className":2070},[575],[577,2072,2073],{"xmlns":579},[581,2074,2075,2091],{},[584,2076,2077,2083,2085],{},[632,2078,2079,2081],{},[587,2080,647],{},[649,2082,651],{},[640,2084,654],{},[632,2086,2087,2089],{},[587,2088,647],{},[587,2090,589],{},[591,2092,965],{"encoding":593},[568,2094,2096,2151],{"className":2095,"ariaHidden":598},[597],[568,2097,2099,2102,2142,2145,2148],{"className":2098},[602],[568,2100],{"className":2101,"style":762},[606],[568,2103,2105,2108],{"className":2104},[611],[568,2106,647],{"className":2107},[611,612],[568,2109,2111],{"className":2110},[697],[568,2112,2114,2134],{"className":2113},[701,702],[568,2115,2117,2131],{"className":2116},[706],[568,2118,2120],{"className":2119,"style":781},[710],[568,2121,2122,2125],{"style":714},[568,2123],{"className":2124,"style":719},[718],[568,2126,2128],{"className":2127},[723,724,725,726],[568,2129,651],{"className":2130},[611,726],[568,2132,734],{"className":2133},[733],[568,2135,2137],{"className":2136},[706],[568,2138,2140],{"className":2139,"style":741},[710],[568,2141],{},[568,2143],{"className":2144,"style":807},[747],[568,2146,654],{"className":2147},[811],[568,2149],{"className":2150,"style":807},[747],[568,2152,2154,2157],{"className":2153},[602],[568,2155],{"className":2156,"style":687},[606],[568,2158,2160,2163],{"className":2159},[611],[568,2161,647],{"className":2162},[611,612],[568,2164,2166],{"className":2165},[697],[568,2167,2169,2189],{"className":2168},[701,702],[568,2170,2172,2186],{"className":2171},[706],[568,2173,2175],{"className":2174,"style":711},[710],[568,2176,2177,2180],{"style":714},[568,2178],{"className":2179,"style":719},[718],[568,2181,2183],{"className":2182},[723,724,725,726],[568,2184,589],{"className":2185},[611,612,726],[568,2187,734],{"className":2188},[733],[568,2190,2192],{"className":2191},[706],[568,2193,2195],{"className":2194,"style":741},[710],[568,2196],{},", denn wenn man im oberen Summanden ",[568,2199,2201,2214],{"className":2200},[571],[568,2202,2204],{"className":2203},[575],[577,2205,2206],{"xmlns":579},[581,2207,2208,2212],{},[584,2209,2210],{},[587,2211,1240],{},[591,2213,1240],{"encoding":593},[568,2215,2217],{"className":2216,"ariaHidden":598},[597],[568,2218,2220,2223],{"className":2219},[602],[568,2221],{"className":2222,"style":1406},[606],[568,2224,1240],{"className":2225},[611,612]," dazuzählt, zieht man im unteren ",[568,2228,2230,2243],{"className":2229},[571],[568,2231,2233],{"className":2232},[575],[577,2234,2235],{"xmlns":579},[581,2236,2237,2241],{},[584,2238,2239],{},[587,2240,1240],{},[591,2242,1240],{"encoding":593},[568,2244,2246],{"className":2245,"ariaHidden":598},[597],[568,2247,2249,2252],{"className":2248},[602],[568,2250],{"className":2251,"style":1406},[606],[568,2253,1240],{"className":2254},[611,612]," ab. Es gibt ",[568,2257,2259,2272],{"className":2258},[571],[568,2260,2262],{"className":2261},[575],[577,2263,2264],{"xmlns":579},[581,2265,2266,2270],{},[584,2267,2268],{},[587,2269,589],{},[591,2271,589],{"encoding":593},[568,2273,2275],{"className":2274,"ariaHidden":598},[597],[568,2276,2278,2281],{"className":2277},[602],[568,2279],{"className":2280,"style":607},[606],[568,2282,589],{"className":2283},[611,612]," Spalten, also ",[568,2286,2288,2332],{"className":2287},[571],[568,2289,2291],{"className":2290},[575],[577,2292,2293],{"xmlns":579},[581,2294,2295,2329],{},[584,2296,2297,2299,2305,2307,2309,2311,2313,2319,2321,2327],{},[649,2298,661],{},[632,2300,2301,2303],{},[587,2302,636],{},[587,2304,589],{},[640,2306,642],{},[587,2308,589],{},[640,2310,1237],{},[640,2312,1224],{"stretchy":1223},[632,2314,2315,2317],{},[587,2316,647],{},[649,2318,651],{},[640,2320,654],{},[632,2322,2323,2325],{},[587,2324,647],{},[587,2326,589],{},[640,2328,1234],{"stretchy":1223},[591,2330,2331],{"encoding":593},"2 s_n = n \\cdot (a_1 + a_n)",[568,2333,2335,2394,2413,2471],{"className":2334,"ariaHidden":598},[597],[568,2336,2338,2342,2345,2385,2388,2391],{"className":2337},[602],[568,2339],{"className":2340,"style":2341},[606],"height:0.7944em;vertical-align:-0.15em;",[568,2343,661],{"className":2344},[611],[568,2346,2348,2351],{"className":2347},[611],[568,2349,636],{"className":2350},[611,612],[568,2352,2354],{"className":2353},[697],[568,2355,2357,2377],{"className":2356},[701,702],[568,2358,2360,2374],{"className":2359},[706],[568,2361,2363],{"className":2362,"style":711},[710],[568,2364,2365,2368],{"style":714},[568,2366],{"className":2367,"style":719},[718],[568,2369,2371],{"className":2370},[723,724,725,726],[568,2372,589],{"className":2373},[611,612,726],[568,2375,734],{"className":2376},[733],[568,2378,2380],{"className":2379},[706],[568,2381,2383],{"className":2382,"style":741},[710],[568,2384],{},[568,2386],{"className":2387,"style":748},[747],[568,2389,642],{"className":2390},[752],[568,2392],{"className":2393,"style":748},[747],[568,2395,2397,2401,2404,2407,2410],{"className":2396},[602],[568,2398],{"className":2399,"style":2400},[606],"height:0.4445em;",[568,2402,589],{"className":2403},[611,612],[568,2405],{"className":2406,"style":807},[747],[568,2408,1237],{"className":2409},[811],[568,2411],{"className":2412,"style":807},[747],[568,2414,2416,2419,2422,2462,2465,2468],{"className":2415},[602],[568,2417],{"className":2418,"style":1363},[606],[568,2420,1224],{"className":2421},[1109],[568,2423,2425,2428],{"className":2424},[611],[568,2426,647],{"className":2427},[611,612],[568,2429,2431],{"className":2430},[697],[568,2432,2434,2454],{"className":2433},[701,702],[568,2435,2437,2451],{"className":2436},[706],[568,2438,2440],{"className":2439,"style":781},[710],[568,2441,2442,2445],{"style":714},[568,2443],{"className":2444,"style":719},[718],[568,2446,2448],{"className":2447},[723,724,725,726],[568,2449,651],{"className":2450},[611,726],[568,2452,734],{"className":2453},[733],[568,2455,2457],{"className":2456},[706],[568,2458,2460],{"className":2459,"style":741},[710],[568,2461],{},[568,2463],{"className":2464,"style":807},[747],[568,2466,654],{"className":2467},[811],[568,2469],{"className":2470,"style":807},[747],[568,2472,2474,2477,2517],{"className":2473},[602],[568,2475],{"className":2476,"style":1363},[606],[568,2478,2480,2483],{"className":2479},[611],[568,2481,647],{"className":2482},[611,612],[568,2484,2486],{"className":2485},[697],[568,2487,2489,2509],{"className":2488},[701,702],[568,2490,2492,2506],{"className":2491},[706],[568,2493,2495],{"className":2494,"style":711},[710],[568,2496,2497,2500],{"style":714},[568,2498],{"className":2499,"style":719},[718],[568,2501,2503],{"className":2502},[723,724,725,726],[568,2504,589],{"className":2505},[611,612,726],[568,2507,734],{"className":2508},[733],[568,2510,2512],{"className":2511},[706],[568,2513,2515],{"className":2514,"style":741},[710],[568,2516],{},[568,2518,1234],{"className":2519},[1181],".",[559,2522,2524],{"id":2523},"beispiele","Beispiele",[564,2526,2527,2528,2558,2559,2651,2652,2651,2703,2520],{},"Die Summe der ersten ",[568,2529,2531,2545],{"className":2530},[571],[568,2532,2534],{"className":2533},[575],[577,2535,2536],{"xmlns":579},[581,2537,2538,2543],{},[584,2539,2540],{},[649,2541,2542],{},"20",[591,2544,2542],{"encoding":593},[568,2546,2548],{"className":2547,"ariaHidden":598},[597],[568,2549,2551,2555],{"className":2550},[602],[568,2552],{"className":2553,"style":2554},[606],"height:0.6444em;",[568,2556,2542],{"className":2557},[611]," ungeraden Zahlen: ",[568,2560,2562,2584],{"className":2561},[571],[568,2563,2565],{"className":2564},[575],[577,2566,2567],{"xmlns":579},[581,2568,2569,2581],{},[584,2570,2571,2577,2579],{},[632,2572,2573,2575],{},[587,2574,647],{},[649,2576,651],{},[640,2578,642],{},[649,2580,651],{},[591,2582,2583],{"encoding":593},"a_1 = 1",[568,2585,2587,2642],{"className":2586,"ariaHidden":598},[597],[568,2588,2590,2593,2633,2636,2639],{"className":2589},[602],[568,2591],{"className":2592,"style":687},[606],[568,2594,2596,2599],{"className":2595},[611],[568,2597,647],{"className":2598},[611,612],[568,2600,2602],{"className":2601},[697],[568,2603,2605,2625],{"className":2604},[701,702],[568,2606,2608,2622],{"className":2607},[706],[568,2609,2611],{"className":2610,"style":781},[710],[568,2612,2613,2616],{"style":714},[568,2614],{"className":2615,"style":719},[718],[568,2617,2619],{"className":2618},[723,724,725,726],[568,2620,651],{"className":2621},[611,726],[568,2623,734],{"className":2624},[733],[568,2626,2628],{"className":2627},[706],[568,2629,2631],{"className":2630,"style":741},[710],[568,2632],{},[568,2634],{"className":2635,"style":748},[747],[568,2637,642],{"className":2638},[752],[568,2640],{"className":2641,"style":748},[747],[568,2643,2645,2648],{"className":2644},[602],[568,2646],{"className":2647,"style":2554},[606],[568,2649,651],{"className":2650},[611],", ",[568,2653,2655,2673],{"className":2654},[571],[568,2656,2658],{"className":2657},[575],[577,2659,2660],{"xmlns":579},[581,2661,2662,2670],{},[584,2663,2664,2666,2668],{},[587,2665,1240],{},[640,2667,642],{},[649,2669,661],{},[591,2671,2672],{"encoding":593},"d = 2",[568,2674,2676,2694],{"className":2675,"ariaHidden":598},[597],[568,2677,2679,2682,2685,2688,2691],{"className":2678},[602],[568,2680],{"className":2681,"style":1406},[606],[568,2683,1240],{"className":2684},[611,612],[568,2686],{"className":2687,"style":748},[747],[568,2689,642],{"className":2690},[752],[568,2692],{"className":2693,"style":748},[747],[568,2695,2697,2700],{"className":2696},[602],[568,2698],{"className":2699,"style":2554},[606],[568,2701,661],{"className":2702},[611],[568,2704,2706,2742],{"className":2705},[571],[568,2707,2709],{"className":2708},[575],[577,2710,2711],{"xmlns":579},[581,2712,2713,2739],{},[584,2714,2715,2721,2723,2725,2727,2730,2732,2734,2736],{},[632,2716,2717,2719],{},[587,2718,647],{},[649,2720,2542],{},[640,2722,642],{},[649,2724,651],{},[640,2726,654],{},[649,2728,2729],{},"19",[640,2731,1237],{},[649,2733,661],{},[640,2735,642],{},[649,2737,2738],{},"39",[591,2740,2741],{"encoding":593},"a_{20} = 1 + 19 \\cdot 2 = 39",[568,2743,2745,2803,2822,2840,2858],{"className":2744,"ariaHidden":598},[597],[568,2746,2748,2751,2794,2797,2800],{"className":2747},[602],[568,2749],{"className":2750,"style":687},[606],[568,2752,2754,2757],{"className":2753},[611],[568,2755,647],{"className":2756},[611,612],[568,2758,2760],{"className":2759},[697],[568,2761,2763,2786],{"className":2762},[701,702],[568,2764,2766,2783],{"className":2765},[706],[568,2767,2769],{"className":2768,"style":781},[710],[568,2770,2771,2774],{"style":714},[568,2772],{"className":2773,"style":719},[718],[568,2775,2777],{"className":2776},[723,724,725,726],[568,2778,2780],{"className":2779},[611,726],[568,2781,2542],{"className":2782},[611,726],[568,2784,734],{"className":2785},[733],[568,2787,2789],{"className":2788},[706],[568,2790,2792],{"className":2791,"style":741},[710],[568,2793],{},[568,2795],{"className":2796,"style":748},[747],[568,2798,642],{"className":2799},[752],[568,2801],{"className":2802,"style":748},[747],[568,2804,2806,2810,2813,2816,2819],{"className":2805},[602],[568,2807],{"className":2808,"style":2809},[606],"height:0.7278em;vertical-align:-0.0833em;",[568,2811,651],{"className":2812},[611],[568,2814],{"className":2815,"style":807},[747],[568,2817,654],{"className":2818},[811],[568,2820],{"className":2821,"style":807},[747],[568,2823,2825,2828,2831,2834,2837],{"className":2824},[602],[568,2826],{"className":2827,"style":2554},[606],[568,2829,2729],{"className":2830},[611],[568,2832],{"className":2833,"style":807},[747],[568,2835,1237],{"className":2836},[811],[568,2838],{"className":2839,"style":807},[747],[568,2841,2843,2846,2849,2852,2855],{"className":2842},[602],[568,2844],{"className":2845,"style":2554},[606],[568,2847,661],{"className":2848},[611],[568,2850],{"className":2851,"style":748},[747],[568,2853,642],{"className":2854},[752],[568,2856],{"className":2857,"style":748},[747],[568,2859,2861,2864],{"className":2860},[602],[568,2862],{"className":2863,"style":2554},[606],[568,2865,2738],{"className":2866},[611],[568,2868,2870],{"className":2869},[1421],[568,2871,2873,2916],{"className":2872},[571],[568,2874,2876],{"className":2875},[575],[577,2877,2878],{"xmlns":579,"display":1430},[581,2879,2880,2913],{},[584,2881,2882,2888,2890,2896,2898,2900,2902,2904,2906,2908,2910],{},[632,2883,2884,2886],{},[587,2885,636],{},[649,2887,2542],{},[640,2889,642],{},[1084,2891,2892,2894],{},[649,2893,2542],{},[649,2895,661],{},[640,2897,1237],{},[640,2899,1224],{"stretchy":1223},[649,2901,651],{},[640,2903,654],{},[649,2905,2738],{},[640,2907,1234],{"stretchy":1223},[640,2909,642],{},[649,2911,2912],{},"400",[591,2914,2915],{"encoding":593},"s_{20} = \\frac{20}{2} \\cdot (1 + 39) = 400",[568,2917,2919,2977,3059,3080,3101],{"className":2918,"ariaHidden":598},[597],[568,2920,2922,2925,2968,2971,2974],{"className":2921},[602],[568,2923],{"className":2924,"style":687},[606],[568,2926,2928,2931],{"className":2927},[611],[568,2929,636],{"className":2930},[611,612],[568,2932,2934],{"className":2933},[697],[568,2935,2937,2960],{"className":2936},[701,702],[568,2938,2940,2957],{"className":2939},[706],[568,2941,2943],{"className":2942,"style":781},[710],[568,2944,2945,2948],{"style":714},[568,2946],{"className":2947,"style":719},[718],[568,2949,2951],{"className":2950},[723,724,725,726],[568,2952,2954],{"className":2953},[611,726],[568,2955,2542],{"className":2956},[611,726],[568,2958,734],{"className":2959},[733],[568,2961,2963],{"className":2962},[706],[568,2964,2966],{"className":2965,"style":741},[710],[568,2967],{},[568,2969],{"className":2970,"style":748},[747],[568,2972,642],{"className":2973},[752],[568,2975],{"className":2976,"style":748},[747],[568,2978,2980,2984,3050,3053,3056],{"className":2979},[602],[568,2981],{"className":2982,"style":2983},[606],"height:2.0074em;vertical-align:-0.686em;",[568,2985,2987,2990,3047],{"className":2986},[611],[568,2988],{"className":2989},[1109,1110],[568,2991,2993],{"className":2992},[1084],[568,2994,2996,3038],{"className":2995},[701,702],[568,2997,2999,3035],{"className":2998},[706],[568,3000,3003,3015,3023],{"className":3001,"style":3002},[710],"height:1.3214em;",[568,3004,3006,3009],{"style":3005},"top:-2.314em;",[568,3007],{"className":3008,"style":1130},[718],[568,3010,3012],{"className":3011},[611],[568,3013,661],{"className":3014},[611],[568,3016,3017,3020],{"style":1142},[568,3018],{"className":3019,"style":1130},[718],[568,3021],{"className":3022,"style":1150},[1149],[568,3024,3026,3029],{"style":3025},"top:-3.677em;",[568,3027],{"className":3028,"style":1130},[718],[568,3030,3032],{"className":3031},[611],[568,3033,2542],{"className":3034},[611],[568,3036,734],{"className":3037},[733],[568,3039,3041],{"className":3040},[706],[568,3042,3045],{"className":3043,"style":3044},[710],"height:0.686em;",[568,3046],{},[568,3048],{"className":3049},[1181,1110],[568,3051],{"className":3052,"style":807},[747],[568,3054,1237],{"className":3055},[811],[568,3057],{"className":3058,"style":807},[747],[568,3060,3062,3065,3068,3071,3074,3077],{"className":3061},[602],[568,3063],{"className":3064,"style":1363},[606],[568,3066,1224],{"className":3067},[1109],[568,3069,651],{"className":3070},[611],[568,3072],{"className":3073,"style":807},[747],[568,3075,654],{"className":3076},[811],[568,3078],{"className":3079,"style":807},[747],[568,3081,3083,3086,3089,3092,3095,3098],{"className":3082},[602],[568,3084],{"className":3085,"style":1363},[606],[568,3087,2738],{"className":3088},[611],[568,3090,1234],{"className":3091},[1181],[568,3093],{"className":3094,"style":748},[747],[568,3096,642],{"className":3097},[752],[568,3099],{"className":3100,"style":748},[747],[568,3102,3104,3107],{"className":3103},[602],[568,3105],{"className":3106,"style":2554},[606],[568,3108,2912],{"className":3109},[611],[564,3111,3112,3113,3142,3143,3172,3173,3201,3202,3299],{},"Ein Saal hat ",[568,3114,3116,3130],{"className":3115},[571],[568,3117,3119],{"className":3118},[575],[577,3120,3121],{"xmlns":579},[581,3122,3123,3128],{},[584,3124,3125],{},[649,3126,3127],{},"25",[591,3129,3127],{"encoding":593},[568,3131,3133],{"className":3132,"ariaHidden":598},[597],[568,3134,3136,3139],{"className":3135},[602],[568,3137],{"className":3138,"style":2554},[606],[568,3140,3127],{"className":3141},[611]," Sitzreihen. In der ersten Reihe stehen ",[568,3144,3146,3160],{"className":3145},[571],[568,3147,3149],{"className":3148},[575],[577,3150,3151],{"xmlns":579},[581,3152,3153,3158],{},[584,3154,3155],{},[649,3156,3157],{},"18",[591,3159,3157],{"encoding":593},[568,3161,3163],{"className":3162,"ariaHidden":598},[597],[568,3164,3166,3169],{"className":3165},[602],[568,3167],{"className":3168,"style":2554},[606],[568,3170,3157],{"className":3171},[611]," Stühle, jede weitere Reihe hat ",[568,3174,3176,3189],{"className":3175},[571],[568,3177,3179],{"className":3178},[575],[577,3180,3181],{"xmlns":579},[581,3182,3183,3187],{},[584,3184,3185],{},[649,3186,661],{},[591,3188,661],{"encoding":593},[568,3190,3192],{"className":3191,"ariaHidden":598},[597],[568,3193,3195,3198],{"className":3194},[602],[568,3196],{"className":3197,"style":2554},[606],[568,3199,661],{"className":3200},[611]," mehr. Die letzte Reihe hat ",[568,3203,3205,3233],{"className":3204},[571],[568,3206,3208],{"className":3207},[575],[577,3209,3210],{"xmlns":579},[581,3211,3212,3230],{},[584,3213,3214,3216,3218,3221,3223,3225,3227],{},[649,3215,3157],{},[640,3217,654],{},[649,3219,3220],{},"24",[640,3222,1237],{},[649,3224,661],{},[640,3226,642],{},[649,3228,3229],{},"66",[591,3231,3232],{"encoding":593},"18 + 24 \\cdot 2 = 66",[568,3234,3236,3254,3272,3290],{"className":3235,"ariaHidden":598},[597],[568,3237,3239,3242,3245,3248,3251],{"className":3238},[602],[568,3240],{"className":3241,"style":2809},[606],[568,3243,3157],{"className":3244},[611],[568,3246],{"className":3247,"style":807},[747],[568,3249,654],{"className":3250},[811],[568,3252],{"className":3253,"style":807},[747],[568,3255,3257,3260,3263,3266,3269],{"className":3256},[602],[568,3258],{"className":3259,"style":2554},[606],[568,3261,3220],{"className":3262},[611],[568,3264],{"className":3265,"style":807},[747],[568,3267,1237],{"className":3268},[811],[568,3270],{"className":3271,"style":807},[747],[568,3273,3275,3278,3281,3284,3287],{"className":3274},[602],[568,3276],{"className":3277,"style":2554},[606],[568,3279,661],{"className":3280},[611],[568,3282],{"className":3283,"style":748},[747],[568,3285,642],{"className":3286},[752],[568,3288],{"className":3289,"style":748},[747],[568,3291,3293,3296],{"className":3292},[602],[568,3294],{"className":3295,"style":2554},[606],[568,3297,3229],{"className":3298},[611]," Stühle, insgesamt sind es",[568,3301,3303],{"className":3302},[1421],[568,3304,3306,3349],{"className":3305},[571],[568,3307,3309],{"className":3308},[575],[577,3310,3311],{"xmlns":579,"display":1430},[581,3312,3313,3346],{},[584,3314,3315,3321,3323,3329,3331,3333,3335,3337,3339,3341,3343],{},[632,3316,3317,3319],{},[587,3318,636],{},[649,3320,3127],{},[640,3322,642],{},[1084,3324,3325,3327],{},[649,3326,3127],{},[649,3328,661],{},[640,3330,1237],{},[640,3332,1224],{"stretchy":1223},[649,3334,3157],{},[640,3336,654],{},[649,3338,3229],{},[640,3340,1234],{"stretchy":1223},[640,3342,642],{},[649,3344,3345],{},"1050",[591,3347,3348],{"encoding":593},"s_{25} = \\frac{25}{2} \\cdot (18 + 66) = 1050",[568,3350,3352,3410,3487,3508,3529],{"className":3351,"ariaHidden":598},[597],[568,3353,3355,3358,3401,3404,3407],{"className":3354},[602],[568,3356],{"className":3357,"style":687},[606],[568,3359,3361,3364],{"className":3360},[611],[568,3362,636],{"className":3363},[611,612],[568,3365,3367],{"className":3366},[697],[568,3368,3370,3393],{"className":3369},[701,702],[568,3371,3373,3390],{"className":3372},[706],[568,3374,3376],{"className":3375,"style":781},[710],[568,3377,3378,3381],{"style":714},[568,3379],{"className":3380,"style":719},[718],[568,3382,3384],{"className":3383},[723,724,725,726],[568,3385,3387],{"className":3386},[611,726],[568,3388,3127],{"className":3389},[611,726],[568,3391,734],{"className":3392},[733],[568,3394,3396],{"className":3395},[706],[568,3397,3399],{"className":3398,"style":741},[710],[568,3400],{},[568,3402],{"className":3403,"style":748},[747],[568,3405,642],{"className":3406},[752],[568,3408],{"className":3409,"style":748},[747],[568,3411,3413,3416,3478,3481,3484],{"className":3412},[602],[568,3414],{"className":3415,"style":2983},[606],[568,3417,3419,3422,3475],{"className":3418},[611],[568,3420],{"className":3421},[1109,1110],[568,3423,3425],{"className":3424},[1084],[568,3426,3428,3467],{"className":3427},[701,702],[568,3429,3431,3464],{"className":3430},[706],[568,3432,3434,3445,3453],{"className":3433,"style":3002},[710],[568,3435,3436,3439],{"style":3005},[568,3437],{"className":3438,"style":1130},[718],[568,3440,3442],{"className":3441},[611],[568,3443,661],{"className":3444},[611],[568,3446,3447,3450],{"style":1142},[568,3448],{"className":3449,"style":1130},[718],[568,3451],{"className":3452,"style":1150},[1149],[568,3454,3455,3458],{"style":3025},[568,3456],{"className":3457,"style":1130},[718],[568,3459,3461],{"className":3460},[611],[568,3462,3127],{"className":3463},[611],[568,3465,734],{"className":3466},[733],[568,3468,3470],{"className":3469},[706],[568,3471,3473],{"className":3472,"style":3044},[710],[568,3474],{},[568,3476],{"className":3477},[1181,1110],[568,3479],{"className":3480,"style":807},[747],[568,3482,1237],{"className":3483},[811],[568,3485],{"className":3486,"style":807},[747],[568,3488,3490,3493,3496,3499,3502,3505],{"className":3489},[602],[568,3491],{"className":3492,"style":1363},[606],[568,3494,1224],{"className":3495},[1109],[568,3497,3157],{"className":3498},[611],[568,3500],{"className":3501,"style":807},[747],[568,3503,654],{"className":3504},[811],[568,3506],{"className":3507,"style":807},[747],[568,3509,3511,3514,3517,3520,3523,3526],{"className":3510},[602],[568,3512],{"className":3513,"style":1363},[606],[568,3515,3229],{"className":3516},[611],[568,3518,1234],{"className":3519},[1181],[568,3521],{"className":3522,"style":748},[747],[568,3524,642],{"className":3525},[752],[568,3527],{"className":3528,"style":748},[747],[568,3530,3532,3535],{"className":3531},[602],[568,3533],{"className":3534,"style":2554},[606],[568,3536,3345],{"className":3537},[611],[564,3539,3540,3541,3570,3571,3599,3600,3629,3630,3705,3706,3734],{},"Summe aller Vielfachen von ",[568,3542,3544,3558],{"className":3543},[571],[568,3545,3547],{"className":3546},[575],[577,3548,3549],{"xmlns":579},[581,3550,3551,3556],{},[584,3552,3553],{},[649,3554,3555],{},"7",[591,3557,3555],{"encoding":593},[568,3559,3561],{"className":3560,"ariaHidden":598},[597],[568,3562,3564,3567],{"className":3563},[602],[568,3565],{"className":3566,"style":2554},[606],[568,3568,3555],{"className":3569},[611]," zwischen ",[568,3572,3574,3587],{"className":3573},[571],[568,3575,3577],{"className":3576},[575],[577,3578,3579],{"xmlns":579},[581,3580,3581,3585],{},[584,3582,3583],{},[649,3584,651],{},[591,3586,651],{"encoding":593},[568,3588,3590],{"className":3589,"ariaHidden":598},[597],[568,3591,3593,3596],{"className":3592},[602],[568,3594],{"className":3595,"style":2554},[606],[568,3597,651],{"className":3598},[611]," und ",[568,3601,3603,3617],{"className":3602},[571],[568,3604,3606],{"className":3605},[575],[577,3607,3608],{"xmlns":579},[581,3609,3610,3615],{},[584,3611,3612],{},[649,3613,3614],{},"500",[591,3616,3614],{"encoding":593},[568,3618,3620],{"className":3619,"ariaHidden":598},[597],[568,3621,3623,3626],{"className":3622},[602],[568,3624],{"className":3625,"style":2554},[606],[568,3627,3614],{"className":3628},[611],": Das größte ist ",[568,3631,3633,3657],{"className":3632},[571],[568,3634,3636],{"className":3635},[575],[577,3637,3638],{"xmlns":579},[581,3639,3640,3654],{},[584,3641,3642,3645,3647,3650,3652],{},[649,3643,3644],{},"497",[640,3646,642],{},[649,3648,3649],{},"71",[640,3651,1237],{},[649,3653,3555],{},[591,3655,3656],{"encoding":593},"497 = 71 \\cdot 7",[568,3658,3660,3678,3696],{"className":3659,"ariaHidden":598},[597],[568,3661,3663,3666,3669,3672,3675],{"className":3662},[602],[568,3664],{"className":3665,"style":2554},[606],[568,3667,3644],{"className":3668},[611],[568,3670],{"className":3671,"style":748},[747],[568,3673,642],{"className":3674},[752],[568,3676],{"className":3677,"style":748},[747],[568,3679,3681,3684,3687,3690,3693],{"className":3680},[602],[568,3682],{"className":3683,"style":2554},[606],[568,3685,3649],{"className":3686},[611],[568,3688],{"className":3689,"style":807},[747],[568,3691,1237],{"className":3692},[811],[568,3694],{"className":3695,"style":807},[747],[568,3697,3699,3702],{"className":3698},[602],[568,3700],{"className":3701,"style":2554},[606],[568,3703,3555],{"className":3704},[611],", also sind es ",[568,3707,3709,3722],{"className":3708},[571],[568,3710,3712],{"className":3711},[575],[577,3713,3714],{"xmlns":579},[581,3715,3716,3720],{},[584,3717,3718],{},[649,3719,3649],{},[591,3721,3649],{"encoding":593},[568,3723,3725],{"className":3724,"ariaHidden":598},[597],[568,3726,3728,3731],{"className":3727},[602],[568,3729],{"className":3730,"style":2554},[606],[568,3732,3649],{"className":3733},[611]," Glieder.",[568,3736,3738],{"className":3737},[1421],[568,3739,3741,3784],{"className":3740},[571],[568,3742,3744],{"className":3743},[575],[577,3745,3746],{"xmlns":579,"display":1430},[581,3747,3748,3781],{},[584,3749,3750,3756,3758,3764,3766,3768,3770,3772,3774,3776,3778],{},[632,3751,3752,3754],{},[587,3753,636],{},[649,3755,3649],{},[640,3757,642],{},[1084,3759,3760,3762],{},[649,3761,3649],{},[649,3763,661],{},[640,3765,1237],{},[640,3767,1224],{"stretchy":1223},[649,3769,3555],{},[640,3771,654],{},[649,3773,3644],{},[640,3775,1234],{"stretchy":1223},[640,3777,642],{},[649,3779,3780],{},"17892",[591,3782,3783],{"encoding":593},"s_{71} = \\frac{71}{2} \\cdot (7 + 497) = 17892",[568,3785,3787,3845,3922,3943,3964],{"className":3786,"ariaHidden":598},[597],[568,3788,3790,3793,3836,3839,3842],{"className":3789},[602],[568,3791],{"className":3792,"style":687},[606],[568,3794,3796,3799],{"className":3795},[611],[568,3797,636],{"className":3798},[611,612],[568,3800,3802],{"className":3801},[697],[568,3803,3805,3828],{"className":3804},[701,702],[568,3806,3808,3825],{"className":3807},[706],[568,3809,3811],{"className":3810,"style":781},[710],[568,3812,3813,3816],{"style":714},[568,3814],{"className":3815,"style":719},[718],[568,3817,3819],{"className":3818},[723,724,725,726],[568,3820,3822],{"className":3821},[611,726],[568,3823,3649],{"className":3824},[611,726],[568,3826,734],{"className":3827},[733],[568,3829,3831],{"className":3830},[706],[568,3832,3834],{"className":3833,"style":741},[710],[568,3835],{},[568,3837],{"className":3838,"style":748},[747],[568,3840,642],{"className":3841},[752],[568,3843],{"className":3844,"style":748},[747],[568,3846,3848,3851,3913,3916,3919],{"className":3847},[602],[568,3849],{"className":3850,"style":2983},[606],[568,3852,3854,3857,3910],{"className":3853},[611],[568,3855],{"className":3856},[1109,1110],[568,3858,3860],{"className":3859},[1084],[568,3861,3863,3902],{"className":3862},[701,702],[568,3864,3866,3899],{"className":3865},[706],[568,3867,3869,3880,3888],{"className":3868,"style":3002},[710],[568,3870,3871,3874],{"style":3005},[568,3872],{"className":3873,"style":1130},[718],[568,3875,3877],{"className":3876},[611],[568,3878,661],{"className":3879},[611],[568,3881,3882,3885],{"style":1142},[568,3883],{"className":3884,"style":1130},[718],[568,3886],{"className":3887,"style":1150},[1149],[568,3889,3890,3893],{"style":3025},[568,3891],{"className":3892,"style":1130},[718],[568,3894,3896],{"className":3895},[611],[568,3897,3649],{"className":3898},[611],[568,3900,734],{"className":3901},[733],[568,3903,3905],{"className":3904},[706],[568,3906,3908],{"className":3907,"style":3044},[710],[568,3909],{},[568,3911],{"className":3912},[1181,1110],[568,3914],{"className":3915,"style":807},[747],[568,3917,1237],{"className":3918},[811],[568,3920],{"className":3921,"style":807},[747],[568,3923,3925,3928,3931,3934,3937,3940],{"className":3924},[602],[568,3926],{"className":3927,"style":1363},[606],[568,3929,1224],{"className":3930},[1109],[568,3932,3555],{"className":3933},[611],[568,3935],{"className":3936,"style":807},[747],[568,3938,654],{"className":3939},[811],[568,3941],{"className":3942,"style":807},[747],[568,3944,3946,3949,3952,3955,3958,3961],{"className":3945},[602],[568,3947],{"className":3948,"style":1363},[606],[568,3950,3644],{"className":3951},[611],[568,3953,1234],{"className":3954},[1181],[568,3956],{"className":3957,"style":748},[747],[568,3959,642],{"className":3960},[752],[568,3962],{"className":3963,"style":748},[747],[568,3965,3967,3970],{"className":3966},[602],[568,3968],{"className":3969,"style":2554},[606],[568,3971,3780],{"className":3972},[611],[559,3974,3976],{"id":3975},"typische-fehler","Typische Fehler",[3978,3979,3980,4152,4226,4359],"ul",{},[3981,3982,3983,3984,4012,4013,4041,4042,4070,4071,4100,4101,2520],"li",{},"Die Anzahl der Glieder falsch bestimmen. Von ",[568,3985,3987,4000],{"className":3986},[571],[568,3988,3990],{"className":3989},[575],[577,3991,3992],{"xmlns":579},[581,3993,3994,3998],{},[584,3995,3996],{},[649,3997,3555],{},[591,3999,3555],{"encoding":593},[568,4001,4003],{"className":4002,"ariaHidden":598},[597],[568,4004,4006,4009],{"className":4005},[602],[568,4007],{"className":4008,"style":2554},[606],[568,4010,3555],{"className":4011},[611]," bis ",[568,4014,4016,4029],{"className":4015},[571],[568,4017,4019],{"className":4018},[575],[577,4020,4021],{"xmlns":579},[581,4022,4023,4027],{},[584,4024,4025],{},[649,4026,3644],{},[591,4028,3644],{"encoding":593},[568,4030,4032],{"className":4031,"ariaHidden":598},[597],[568,4033,4035,4038],{"className":4034},[602],[568,4036],{"className":4037,"style":2554},[606],[568,4039,3644],{"className":4040},[611]," in Siebenerschritten sind es ",[568,4043,4045,4058],{"className":4044},[571],[568,4046,4048],{"className":4047},[575],[577,4049,4050],{"xmlns":579},[581,4051,4052,4056],{},[584,4053,4054],{},[649,4055,3649],{},[591,4057,3649],{"encoding":593},[568,4059,4061],{"className":4060,"ariaHidden":598},[597],[568,4062,4064,4067],{"className":4063},[602],[568,4065],{"className":4066,"style":2554},[606],[568,4068,3649],{"className":4069},[611]," Zahlen, nicht ",[568,4072,4074,4088],{"className":4073},[571],[568,4075,4077],{"className":4076},[575],[577,4078,4079],{"xmlns":579},[581,4080,4081,4086],{},[584,4082,4083],{},[649,4084,4085],{},"70",[591,4087,4085],{"encoding":593},[568,4089,4091],{"className":4090,"ariaHidden":598},[597],[568,4092,4094,4097],{"className":4093},[602],[568,4095],{"className":4096,"style":2554},[606],[568,4098,4085],{"className":4099},[611]," und nicht ",[568,4102,4104,4122],{"className":4103},[571],[568,4105,4107],{"className":4106},[575],[577,4108,4109],{"xmlns":579},[581,4110,4111,4119],{},[584,4112,4113,4115,4117],{},[649,4114,3644],{},[640,4116,1229],{},[649,4118,3555],{},[591,4120,4121],{"encoding":593},"497 - 7",[568,4123,4125,4143],{"className":4124,"ariaHidden":598},[597],[568,4126,4128,4131,4134,4137,4140],{"className":4127},[602],[568,4129],{"className":4130,"style":2809},[606],[568,4132,3644],{"className":4133},[611],[568,4135],{"className":4136,"style":807},[747],[568,4138,1229],{"className":4139},[811],[568,4141],{"className":4142,"style":807},[747],[568,4144,4146,4149],{"className":4145},[602],[568,4147],{"className":4148,"style":2554},[606],[568,4150,3555],{"className":4151},[611],[3981,4153,4154,4155,4225],{},"Für ",[568,4156,4158,4176],{"className":4157},[571],[568,4159,4161],{"className":4160},[575],[577,4162,4163],{"xmlns":579},[581,4164,4165,4173],{},[584,4166,4167],{},[632,4168,4169,4171],{},[587,4170,647],{},[587,4172,589],{},[591,4174,4175],{"encoding":593},"a_n",[568,4177,4179],{"className":4178,"ariaHidden":598},[597],[568,4180,4182,4185],{"className":4181},[602],[568,4183],{"className":4184,"style":687},[606],[568,4186,4188,4191],{"className":4187},[611],[568,4189,647],{"className":4190},[611,612],[568,4192,4194],{"className":4193},[697],[568,4195,4197,4217],{"className":4196},[701,702],[568,4198,4200,4214],{"className":4199},[706],[568,4201,4203],{"className":4202,"style":711},[710],[568,4204,4205,4208],{"style":714},[568,4206],{"className":4207,"style":719},[718],[568,4209,4211],{"className":4210},[723,724,725,726],[568,4212,589],{"className":4213},[611,612,726],[568,4215,734],{"className":4216},[733],[568,4218,4220],{"className":4219},[706],[568,4221,4223],{"className":4222,"style":741},[710],[568,4224],{}," das Glied nach dem letzten einsetzen.",[3981,4227,4228,4229,4291,4292,4358],{},"In der zweiten Form ",[568,4230,4232,4251],{"className":4231},[571],[568,4233,4235],{"className":4234},[575],[577,4236,4237],{"xmlns":579},[581,4238,4239,4248],{},[584,4240,4241],{},[4242,4243,4244,4246],"msup",{},[587,4245,589],{},[649,4247,661],{},[591,4249,4250],{"encoding":593},"n^2",[568,4252,4254],{"className":4253,"ariaHidden":598},[597],[568,4255,4257,4261],{"className":4256},[602],[568,4258],{"className":4259,"style":4260},[606],"height:0.8141em;",[568,4262,4264,4267],{"className":4263},[611],[568,4265,589],{"className":4266},[611,612],[568,4268,4270],{"className":4269},[697],[568,4271,4273],{"className":4272},[701],[568,4274,4276],{"className":4275},[706],[568,4277,4279],{"className":4278,"style":4260},[710],[568,4280,4282,4285],{"style":4281},"top:-3.063em;margin-right:0.05em;",[568,4283],{"className":4284,"style":719},[718],[568,4286,4288],{"className":4287},[723,724,725,726],[568,4289,661],{"className":4290},[611,726]," statt ",[568,4293,4295,4319],{"className":4294},[571],[568,4296,4298],{"className":4297},[575],[577,4299,4300],{"xmlns":579},[581,4301,4302,4316],{},[584,4303,4304,4306,4308,4310,4312,4314],{},[587,4305,589],{},[640,4307,1224],{"stretchy":1223},[587,4309,589],{},[640,4311,1229],{},[649,4313,651],{},[640,4315,1234],{"stretchy":1223},[591,4317,4318],{"encoding":593},"n(n - 1)",[568,4320,4322,4346],{"className":4321,"ariaHidden":598},[597],[568,4323,4325,4328,4331,4334,4337,4340,4343],{"className":4324},[602],[568,4326],{"className":4327,"style":1363},[606],[568,4329,589],{"className":4330},[611,612],[568,4332,1224],{"className":4333},[1109],[568,4335,589],{"className":4336},[611,612],[568,4338],{"className":4339,"style":807},[747],[568,4341,1229],{"className":4342},[811],[568,4344],{"className":4345,"style":807},[747],[568,4347,4349,4352,4355],{"className":4348},[602],[568,4350],{"className":4351,"style":1363},[606],[568,4353,651],{"className":4354},[611],[568,4356,1234],{"className":4357},[1181]," schreiben.",[3981,4360,4361],{},"Die Formel auf Folgen anwenden, die nicht arithmetisch sind, z.B. Quadratzahlen.",{"title":4363,"searchDepth":4364,"depth":4364,"links":4365},"",2,[4366,4367,4368,4369],{"id":561,"depth":4364,"text":562},{"id":1413,"depth":4364,"text":1414},{"id":2523,"depth":4364,"text":2524},{"id":3975,"depth":4364,"text":3976},[4371,4374,4377,4379,4381,4383,4385,4387,4391,4393,4395],{"lhs":4372,"rhs":4373},"n\u002F2*(a1 + (a1 + (n - 1)*d))","n*a1 + n*(n - 1)\u002F2*d",{"lhs":4375,"rhs":4376},"(n + 1)*a1 + (n + 1)*n\u002F2*d","n*a1 + n*(n - 1)\u002F2*d + (a1 + n*d)",{"lhs":4378,"rhs":2738},"1 + 19*2",{"lhs":4380,"rhs":2912},"20\u002F2*(1 + 39)",{"lhs":4382,"rhs":2912},"sum(1:2:39)",{"lhs":4384,"rhs":3229},"18 + 24*2",{"lhs":4386,"rhs":3345},"25\u002F2*(18 + 66)",{"lhs":4373,"rhs":3345,"where":4388},{"n":4389,"a1":4390,"d":4364},25,18,{"lhs":4392,"rhs":3649},"497\u002F7",{"lhs":4394,"rhs":3780},"71\u002F2*(7 + 497)",{"lhs":4396,"rhs":3780},"sum(7:7:497)","n \\in \\mathbb{N},\\ n \\geq 1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">N\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\in \\mathbb{N},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">N\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>n\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\geq 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:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","arithmetic-series","s_n = \\frac{n}{2} \\cdot (a_1 + a_n) = n \\cdot a_1 + \\frac{n(n - 1)}{2} \\cdot d","\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>\u003Cmsub>\u003Cmi>s\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>n\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>+\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>+\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>d\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">s_n = \\frac{n}{2} \\cdot (a_1 + a_n) = n \\cdot a_1 + \\frac{n(n - 1)}{2} \\cdot d\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:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">s\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.7936em;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:1.1076em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\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\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\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\" 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