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usw.:",[569,893,896],{"className":894},[895],"katex-display",[569,897,899,963],{"className":898},[572],[569,900,902],{"className":901},[576],[578,903,905],{"xmlns":580,"display":904},"block",[582,906,907,960],{},[585,908,909,911,914,916,919,922,924,927,929,931,934,936,938,940,942,944,946,948,951,953,956,958],{},[588,910,590],{},[790,912,913],{},"+",[588,915,756],{},[790,917,918],{},"=",[588,920,921],{},"101",[790,923,792],{"separator":599},[839,925],{"width":926},"1em",[588,928,690],{},[790,930,913],{},[588,932,933],{},"99",[790,935,918],{},[588,937,921],{},[790,939,792],{"separator":599},[839,941],{"width":926},[790,943,815],{},[790,945,792],{"separator":599},[839,947],{"width":926},[588,949,950],{},"50",[790,952,913],{},[588,954,955],{},"51",[790,957,918],{},[588,959,921],{},[592,961,962],{"encoding":594},"1 + 100 = 101, \\quad 2 + 99 = 101, \\quad \\ldots, \\quad 50 + 51 = 101",[569,964,966,987,1007,1038,1056,1101,1119],{"className":965,"ariaHidden":599},[598],[569,967,969,973,976,980,984],{"className":968},[603],[569,970],{"className":971,"style":972},[607],"height:0.7278em;vertical-align:-0.0833em;",[569,974,590],{"className":975},[612],[569,977],{"className":978,"style":979},[839],"margin-right:0.2222em;",[569,981,913],{"className":982},[983],"mbin",[569,985],{"className":986,"style":979},[839],[569,988,990,993,996,1000,1004],{"className":989},[603],[569,991],{"className":992,"style":608},[607],[569,994,756],{"className":995},[612],[569,997],{"className":998,"style":999},[839],"margin-right:0.2778em;",[569,1001,918],{"className":1002},[1003],"mrel",[569,1005],{"className":1006,"style":999},[839],[569,1008,1010,1013,1016,1019,1023,1026,1029,1032,1035],{"className":1009},[603],[569,1011],{"className":1012,"style":828},[607],[569,1014,921],{"className":1015},[612],[569,1017,792],{"className":1018},[835],[569,1020],{"className":1021,"style":1022},[839],"margin-right:1em;",[569,1024],{"className":1025,"style":840},[839],[569,1027,690],{"className":1028},[612],[569,1030],{"className":1031,"style":979},[839],[569,1033,913],{"className":1034},[983],[569,1036],{"className":1037,"style":979},[839],[569,1039,1041,1044,1047,1050,1053],{"className":1040},[603],[569,1042],{"className":1043,"style":608},[607],[569,1045,933],{"className":1046},[612],[569,1048],{"className":1049,"style":999},[839],[569,1051,918],{"className":1052},[1003],[569,1054],{"className":1055,"style":999},[839],[569,1057,1059,1062,1065,1068,1071,1074,1077,1080,1083,1086,1089,1092,1095,1098],{"className":1058},[603],[569,1060],{"className":1061,"style":828},[607],[569,1063,921],{"className":1064},[612],[569,1066,792],{"className":1067},[835],[569,1069],{"className":1070,"style":1022},[839],[569,1072],{"className":1073,"style":840},[839],[569,1075,815],{"className":1076},[880],[569,1078],{"className":1079,"style":840},[839],[569,1081,792],{"className":1082},[835],[569,1084],{"className":1085,"style":1022},[839],[569,1087],{"className":1088,"style":840},[839],[569,1090,950],{"className":1091},[612],[569,1093],{"className":1094,"style":979},[839],[569,1096,913],{"className":1097},[983],[569,1099],{"className":1100,"style":979},[839],[569,1102,1104,1107,1110,1113,1116],{"className":1103},[603],[569,1105],{"className":1106,"style":608},[607],[569,1108,955],{"className":1109},[612],[569,1111],{"className":1112,"style":999},[839],[569,1114,918],{"className":1115},[1003],[569,1117],{"className":1118,"style":999},[839],[569,1120,1122,1125],{"className":1121},[603],[569,1123],{"className":1124,"style":608},[607],[569,1126,921],{"className":1127},[612],[565,1129,1130,1131,1183,1184,1306,1307,1464,1465,1493],{},"Jedes Paar ergibt ",[569,1132,1134,1152],{"className":1133},[572],[569,1135,1137],{"className":1136},[576],[578,1138,1139],{"xmlns":580},[582,1140,1141,1149],{},[585,1142,1143,1145,1147],{},[627,1144,629],{},[790,1146,913],{},[588,1148,590],{},[592,1150,1151],{"encoding":594},"n + 1",[569,1153,1155,1174],{"className":1154,"ariaHidden":599},[598],[569,1156,1158,1162,1165,1168,1171],{"className":1157},[603],[569,1159],{"className":1160,"style":1161},[607],"height:0.6667em;vertical-align:-0.0833em;",[569,1163,629],{"className":1164},[612,645],[569,1166],{"className":1167,"style":979},[839],[569,1169,913],{"className":1170},[983],[569,1172],{"className":1173,"style":979},[839],[569,1175,1177,1180],{"className":1176},[603],[569,1178],{"className":1179,"style":608},[607],[569,1181,590],{"className":1182},[612],". Es gibt halb so viele Paare wie Zahlen, also ",[569,1185,1187,1206],{"className":1186},[572],[569,1188,1190],{"className":1189},[576],[578,1191,1192],{"xmlns":580},[582,1193,1194,1203],{},[585,1195,1196],{},[1197,1198,1199,1201],"mfrac",{},[627,1200,629],{},[588,1202,690],{},[592,1204,1205],{"encoding":594},"\\frac{n}{2}",[569,1207,1209],{"className":1208,"ariaHidden":599},[598],[569,1210,1212,1216],{"className":1211},[603],[569,1213],{"className":1214,"style":1215},[607],"height:1.0404em;vertical-align:-0.345em;",[569,1217,1219,1224,1302],{"className":1218},[612],[569,1220],{"className":1221},[1222,1223],"mopen","nulldelimiter",[569,1225,1227],{"className":1226},[1197],[569,1228,1232,1293],{"className":1229},[1230,1231],"vlist-t","vlist-t2",[569,1233,1236,1288],{"className":1234},[1235],"vlist-r",[569,1237,1241,1262,1273],{"className":1238,"style":1240},[1239],"vlist","height:0.6954em;",[569,1242,1244,1249],{"style":1243},"top:-2.655em;",[569,1245],{"className":1246,"style":1248},[1247],"pstrut","height:3em;",[569,1250,1256],{"className":1251},[1252,1253,1254,1255],"sizing","reset-size6","size3","mtight",[569,1257,1259],{"className":1258},[612,1255],[569,1260,690],{"className":1261},[612,1255],[569,1263,1265,1268],{"style":1264},"top:-3.23em;",[569,1266],{"className":1267,"style":1248},[1247],[569,1269],{"className":1270,"style":1272},[1271],"frac-line","border-bottom-width:0.04em;",[569,1274,1276,1279],{"style":1275},"top:-3.394em;",[569,1277],{"className":1278,"style":1248},[1247],[569,1280,1282],{"className":1281},[1252,1253,1254,1255],[569,1283,1285],{"className":1284},[612,1255],[569,1286,629],{"className":1287},[612,645,1255],[569,1289,1292],{"className":1290},[1291],"vlist-s","​",[569,1294,1296],{"className":1295},[1235],[569,1297,1300],{"className":1298,"style":1299},[1239],"height:0.345em;",[569,1301],{},[569,1303],{"className":1304},[1305,1223],"mclose"," Paare. Zusammen sind das ",[569,1308,1310,1344],{"className":1309},[572],[569,1311,1313],{"className":1312},[576],[578,1314,1315],{"xmlns":580},[582,1316,1317,1341],{},[585,1318,1319,1325,1328,1332,1334,1336,1338],{},[1197,1320,1321,1323],{},[627,1322,629],{},[588,1324,690],{},[790,1326,1327],{},"⋅",[790,1329,1331],{"stretchy":1330},"false","(",[627,1333,629],{},[790,1335,913],{},[588,1337,590],{},[790,1339,1340],{"stretchy":1330},")",[592,1342,1343],{"encoding":594},"\\frac{n}{2} \\cdot (n + 1)",[569,1345,1347,1430,1452],{"className":1346,"ariaHidden":599},[598],[569,1348,1350,1353,1421,1424,1427],{"className":1349},[603],[569,1351],{"className":1352,"style":1215},[607],[569,1354,1356,1359,1418],{"className":1355},[612],[569,1357],{"className":1358},[1222,1223],[569,1360,1362],{"className":1361},[1197],[569,1363,1365,1410],{"className":1364},[1230,1231],[569,1366,1368,1407],{"className":1367},[1235],[569,1369,1371,1385,1393],{"className":1370,"style":1240},[1239],[569,1372,1373,1376],{"style":1243},[569,1374],{"className":1375,"style":1248},[1247],[569,1377,1379],{"className":1378},[1252,1253,1254,1255],[569,1380,1382],{"className":1381},[612,1255],[569,1383,690],{"className":1384},[612,1255],[569,1386,1387,1390],{"style":1264},[569,1388],{"className":1389,"style":1248},[1247],[569,1391],{"className":1392,"style":1272},[1271],[569,1394,1395,1398],{"style":1275},[569,1396],{"className":1397,"style":1248},[1247],[569,1399,1401],{"className":1400},[1252,1253,1254,1255],[569,1402,1404],{"className":1403},[612,1255],[569,1405,629],{"className":1406},[612,645,1255],[569,1408,1292],{"className":1409},[1291],[569,1411,1413],{"className":1412},[1235],[569,1414,1416],{"className":1415,"style":1299},[1239],[569,1417],{},[569,1419],{"className":1420},[1305,1223],[569,1422],{"className":1423,"style":979},[839],[569,1425,1327],{"className":1426},[983],[569,1428],{"className":1429,"style":979},[839],[569,1431,1433,1437,1440,1443,1446,1449],{"className":1432},[603],[569,1434],{"className":1435,"style":1436},[607],"height:1em;vertical-align:-0.25em;",[569,1438,1331],{"className":1439},[1222],[569,1441,629],{"className":1442},[612,645],[569,1444],{"className":1445,"style":979},[839],[569,1447,913],{"className":1448},[983],[569,1450],{"className":1451,"style":979},[839],[569,1453,1455,1458,1461],{"className":1454},[603],[569,1456],{"className":1457,"style":1436},[607],[569,1459,590],{"className":1460},[612],[569,1462,1340],{"className":1463},[1305],". Das funktioniert auch für ungerade ",[569,1466,1468,1481],{"className":1467},[572],[569,1469,1471],{"className":1470},[576],[578,1472,1473],{"xmlns":580},[582,1474,1475,1479],{},[585,1476,1477],{},[627,1478,629],{},[592,1480,629],{"encoding":594},[569,1482,1484],{"className":1483,"ariaHidden":599},[598],[569,1485,1487,1490],{"className":1486},[603],[569,1488],{"className":1489,"style":641},[607],[569,1491,629],{"className":1492},[612,645],", wie man durch Nachrechnen sieht.",[560,1495,1497],{"id":1496},"beispiele","Beispiele",[565,1499,1500,1501,613,1529,1557],{},"Die Zahlen von ",[569,1502,1504,1517],{"className":1503},[572],[569,1505,1507],{"className":1506},[576],[578,1508,1509],{"xmlns":580},[582,1510,1511,1515],{},[585,1512,1513],{},[588,1514,590],{},[592,1516,590],{"encoding":594},[569,1518,1520],{"className":1519,"ariaHidden":599},[598],[569,1521,1523,1526],{"className":1522},[603],[569,1524],{"className":1525,"style":608},[607],[569,1527,590],{"className":1528},[612],[569,1530,1532,1545],{"className":1531},[572],[569,1533,1535],{"className":1534},[576],[578,1536,1537],{"xmlns":580},[582,1538,1539,1543],{},[585,1540,1541],{},[588,1542,756],{},[592,1544,756],{"encoding":594},[569,1546,1548],{"className":1547,"ariaHidden":599},[598],[569,1549,1551,1554],{"className":1550},[603],[569,1552],{"className":1553,"style":608},[607],[569,1555,756],{"className":1556},[612],":",[569,1559,1561],{"className":1560},[895],[569,1562,1564,1609],{"className":1563},[572],[569,1565,1567],{"className":1566},[576],[578,1568,1569],{"xmlns":580,"display":904},[582,1570,1571,1606],{},[585,1572,1573,1575,1577,1579,1581,1583,1585,1587,1589,1601,1603],{},[588,1574,590],{},[790,1576,913],{},[588,1578,690],{},[790,1580,913],{},[790,1582,815],{},[790,1584,913],{},[588,1586,756],{},[790,1588,918],{},[1197,1590,1591,1599],{},[585,1592,1593,1595,1597],{},[588,1594,756],{},[790,1596,1327],{},[588,1598,921],{},[588,1600,690],{},[790,1602,918],{},[588,1604,1605],{},"5050",[592,1607,1608],{"encoding":594},"1 + 2 + \\ldots + 100 = \\frac{100 \\cdot 101}{2} = 5050",[569,1610,1612,1630,1648,1666,1684,1778],{"className":1611,"ariaHidden":599},[598],[569,1613,1615,1618,1621,1624,1627],{"className":1614},[603],[569,1616],{"className":1617,"style":972},[607],[569,1619,590],{"className":1620},[612],[569,1622],{"className":1623,"style":979},[839],[569,1625,913],{"className":1626},[983],[569,1628],{"className":1629,"style":979},[839],[569,1631,1633,1636,1639,1642,1645],{"className":1632},[603],[569,1634],{"className":1635,"style":972},[607],[569,1637,690],{"className":1638},[612],[569,1640],{"className":1641,"style":979},[839],[569,1643,913],{"className":1644},[983],[569,1646],{"className":1647,"style":979},[839],[569,1649,1651,1654,1657,1660,1663],{"className":1650},[603],[569,1652],{"className":1653,"style":1161},[607],[569,1655,815],{"className":1656},[880],[569,1658],{"className":1659,"style":979},[839],[569,1661,913],{"className":1662},[983],[569,1664],{"className":1665,"style":979},[839],[569,1667,1669,1672,1675,1678,1681],{"className":1668},[603],[569,1670],{"className":1671,"style":608},[607],[569,1673,756],{"className":1674},[612],[569,1676],{"className":1677,"style":999},[839],[569,1679,918],{"className":1680},[1003],[569,1682],{"className":1683,"style":999},[839],[569,1685,1687,1691,1769,1772,1775],{"className":1686},[603],[569,1688],{"className":1689,"style":1690},[607],"height:2.0074em;vertical-align:-0.686em;",[569,1692,1694,1697,1766],{"className":1693},[612],[569,1695],{"className":1696},[1222,1223],[569,1698,1700],{"className":1699},[1197],[569,1701,1703,1757],{"className":1702},[1230,1231],[569,1704,1706,1754],{"className":1705},[1235],[569,1707,1710,1722,1730],{"className":1708,"style":1709},[1239],"height:1.3214em;",[569,1711,1713,1716],{"style":1712},"top:-2.314em;",[569,1714],{"className":1715,"style":1248},[1247],[569,1717,1719],{"className":1718},[612],[569,1720,690],{"className":1721},[612],[569,1723,1724,1727],{"style":1264},[569,1725],{"className":1726,"style":1248},[1247],[569,1728],{"className":1729,"style":1272},[1271],[569,1731,1733,1736],{"style":1732},"top:-3.677em;",[569,1734],{"className":1735,"style":1248},[1247],[569,1737,1739,1742,1745,1748,1751],{"className":1738},[612],[569,1740,756],{"className":1741},[612],[569,1743],{"className":1744,"style":979},[839],[569,1746,1327],{"className":1747},[983],[569,1749],{"className":1750,"style":979},[839],[569,1752,921],{"className":1753},[612],[569,1755,1292],{"className":1756},[1291],[569,1758,1760],{"className":1759},[1235],[569,1761,1764],{"className":1762,"style":1763},[1239],"height:0.686em;",[569,1765],{},[569,1767],{"className":1768},[1305,1223],[569,1770],{"className":1771,"style":999},[839],[569,1773,918],{"className":1774},[1003],[569,1776],{"className":1777,"style":999},[839],[569,1779,1781,1784],{"className":1780},[603],[569,1782],{"className":1783,"style":608},[607],[569,1785,1605],{"className":1786},[612],[565,1788,1500,1789,613,1817,1557],{},[569,1790,1792,1805],{"className":1791},[572],[569,1793,1795],{"className":1794},[576],[578,1796,1797],{"xmlns":580},[582,1798,1799,1803],{},[585,1800,1801],{},[588,1802,590],{},[592,1804,590],{"encoding":594},[569,1806,1808],{"className":1807,"ariaHidden":599},[598],[569,1809,1811,1814],{"className":1810},[603],[569,1812],{"className":1813,"style":608},[607],[569,1815,590],{"className":1816},[612],[569,1818,1820,1834],{"className":1819},[572],[569,1821,1823],{"className":1822},[576],[578,1824,1825],{"xmlns":580},[582,1826,1827,1832],{},[585,1828,1829],{},[588,1830,1831],{},"40",[592,1833,1831],{"encoding":594},[569,1835,1837],{"className":1836,"ariaHidden":599},[598],[569,1838,1840,1843],{"className":1839},[603],[569,1841],{"className":1842,"style":608},[607],[569,1844,1831],{"className":1845},[612],[569,1847,1849],{"className":1848},[895],[569,1850,1852,1882],{"className":1851},[572],[569,1853,1855],{"className":1854},[576],[578,1856,1857],{"xmlns":580,"display":904},[582,1858,1859,1879],{},[585,1860,1861,1874,1876],{},[1197,1862,1863,1872],{},[585,1864,1865,1867,1869],{},[588,1866,1831],{},[790,1868,1327],{},[588,1870,1871],{},"41",[588,1873,690],{},[790,1875,918],{},[588,1877,1878],{},"820",[592,1880,1881],{"encoding":594},"\\frac{40 \\cdot 41}{2} = 820",[569,1883,1885,1974],{"className":1884,"ariaHidden":599},[598],[569,1886,1888,1891,1965,1968,1971],{"className":1887},[603],[569,1889],{"className":1890,"style":1690},[607],[569,1892,1894,1897,1962],{"className":1893},[612],[569,1895],{"className":1896},[1222,1223],[569,1898,1900],{"className":1899},[1197],[569,1901,1903,1954],{"className":1902},[1230,1231],[569,1904,1906,1951],{"className":1905},[1235],[569,1907,1909,1920,1928],{"className":1908,"style":1709},[1239],[569,1910,1911,1914],{"style":1712},[569,1912],{"className":1913,"style":1248},[1247],[569,1915,1917],{"className":1916},[612],[569,1918,690],{"className":1919},[612],[569,1921,1922,1925],{"style":1264},[569,1923],{"className":1924,"style":1248},[1247],[569,1926],{"className":1927,"style":1272},[1271],[569,1929,1930,1933],{"style":1732},[569,1931],{"className":1932,"style":1248},[1247],[569,1934,1936,1939,1942,1945,1948],{"className":1935},[612],[569,1937,1831],{"className":1938},[612],[569,1940],{"className":1941,"style":979},[839],[569,1943,1327],{"className":1944},[983],[569,1946],{"className":1947,"style":979},[839],[569,1949,1871],{"className":1950},[612],[569,1952,1292],{"className":1953},[1291],[569,1955,1957],{"className":1956},[1235],[569,1958,1960],{"className":1959,"style":1763},[1239],[569,1961],{},[569,1963],{"className":1964},[1305,1223],[569,1966],{"className":1967,"style":999},[839],[569,1969,918],{"className":1970},[1003],[569,1972],{"className":1973,"style":999},[839],[569,1975,1977,1980],{"className":1976},[603],[569,1978],{"className":1979,"style":608},[607],[569,1981,1878],{"className":1982},[612],[565,1984,1500,1985,613,2013,2041,2042,2070,2071,2099],{},[569,1986,1988,2001],{"className":1987},[572],[569,1989,1991],{"className":1990},[576],[578,1992,1993],{"xmlns":580},[582,1994,1995,1999],{},[585,1996,1997],{},[588,1998,955],{},[592,2000,955],{"encoding":594},[569,2002,2004],{"className":2003,"ariaHidden":599},[598],[569,2005,2007,2010],{"className":2006},[603],[569,2008],{"className":2009,"style":608},[607],[569,2011,955],{"className":2012},[612],[569,2014,2016,2029],{"className":2015},[572],[569,2017,2019],{"className":2018},[576],[578,2020,2021],{"xmlns":580},[582,2022,2023,2027],{},[585,2024,2025],{},[588,2026,756],{},[592,2028,756],{"encoding":594},[569,2030,2032],{"className":2031,"ariaHidden":599},[598],[569,2033,2035,2038],{"className":2034},[603],[569,2036],{"className":2037,"style":608},[607],[569,2039,756],{"className":2040},[612],": Man rechnet die Summe bis ",[569,2043,2045,2058],{"className":2044},[572],[569,2046,2048],{"className":2047},[576],[578,2049,2050],{"xmlns":580},[582,2051,2052,2056],{},[585,2053,2054],{},[588,2055,756],{},[592,2057,756],{"encoding":594},[569,2059,2061],{"className":2060,"ariaHidden":599},[598],[569,2062,2064,2067],{"className":2063},[603],[569,2065],{"className":2066,"style":608},[607],[569,2068,756],{"className":2069},[612]," und zieht die Summe bis ",[569,2072,2074,2087],{"className":2073},[572],[569,2075,2077],{"className":2076},[576],[578,2078,2079],{"xmlns":580},[582,2080,2081,2085],{},[585,2082,2083],{},[588,2084,950],{},[592,2086,950],{"encoding":594},[569,2088,2090],{"className":2089,"ariaHidden":599},[598],[569,2091,2093,2096],{"className":2092},[603],[569,2094],{"className":2095,"style":608},[607],[569,2097,950],{"className":2098},[612]," ab.",[569,2101,2103],{"className":2102},[895],[569,2104,2106,2149],{"className":2105},[572],[569,2107,2109],{"className":2108},[576],[578,2110,2111],{"xmlns":580,"display":904},[582,2112,2113,2146],{},[585,2114,2115,2117,2120,2132,2134,2136,2138,2141,2143],{},[588,2116,1605],{},[790,2118,2119],{},"−",[1197,2121,2122,2130],{},[585,2123,2124,2126,2128],{},[588,2125,950],{},[790,2127,1327],{},[588,2129,955],{},[588,2131,690],{},[790,2133,918],{},[588,2135,1605],{},[790,2137,2119],{},[588,2139,2140],{},"1275",[790,2142,918],{},[588,2144,2145],{},"3775",[592,2147,2148],{"encoding":594},"5050 - \\frac{50 \\cdot 51}{2} = 5050 - 1275 = 3775",[569,2150,2152,2170,2259,2277,2295],{"className":2151,"ariaHidden":599},[598],[569,2153,2155,2158,2161,2164,2167],{"className":2154},[603],[569,2156],{"className":2157,"style":972},[607],[569,2159,1605],{"className":2160},[612],[569,2162],{"className":2163,"style":979},[839],[569,2165,2119],{"className":2166},[983],[569,2168],{"className":2169,"style":979},[839],[569,2171,2173,2176,2250,2253,2256],{"className":2172},[603],[569,2174],{"className":2175,"style":1690},[607],[569,2177,2179,2182,2247],{"className":2178},[612],[569,2180],{"className":2181},[1222,1223],[569,2183,2185],{"className":2184},[1197],[569,2186,2188,2239],{"className":2187},[1230,1231],[569,2189,2191,2236],{"className":2190},[1235],[569,2192,2194,2205,2213],{"className":2193,"style":1709},[1239],[569,2195,2196,2199],{"style":1712},[569,2197],{"className":2198,"style":1248},[1247],[569,2200,2202],{"className":2201},[612],[569,2203,690],{"className":2204},[612],[569,2206,2207,2210],{"style":1264},[569,2208],{"className":2209,"style":1248},[1247],[569,2211],{"className":2212,"style":1272},[1271],[569,2214,2215,2218],{"style":1732},[569,2216],{"className":2217,"style":1248},[1247],[569,2219,2221,2224,2227,2230,2233],{"className":2220},[612],[569,2222,950],{"className":2223},[612],[569,2225],{"className":2226,"style":979},[839],[569,2228,1327],{"className":2229},[983],[569,2231],{"className":2232,"style":979},[839],[569,2234,955],{"className":2235},[612],[569,2237,1292],{"className":2238},[1291],[569,2240,2242],{"className":2241},[1235],[569,2243,2245],{"className":2244,"style":1763},[1239],[569,2246],{},[569,2248],{"className":2249},[1305,1223],[569,2251],{"className":2252,"style":999},[839],[569,2254,918],{"className":2255},[1003],[569,2257],{"className":2258,"style":999},[839],[569,2260,2262,2265,2268,2271,2274],{"className":2261},[603],[569,2263],{"className":2264,"style":972},[607],[569,2266,1605],{"className":2267},[612],[569,2269],{"className":2270,"style":979},[839],[569,2272,2119],{"className":2273},[983],[569,2275],{"className":2276,"style":979},[839],[569,2278,2280,2283,2286,2289,2292],{"className":2279},[603],[569,2281],{"className":2282,"style":608},[607],[569,2284,2140],{"className":2285},[612],[569,2287],{"className":2288,"style":999},[839],[569,2290,918],{"className":2291},[1003],[569,2293],{"className":2294,"style":999},[839],[569,2296,2298,2301],{"className":2297},[603],[569,2299],{"className":2300,"style":608},[607],[569,2302,2145],{"className":2303},[612],[560,2305,2307],{"id":2306},"typische-fehler","Typische Fehler",[2309,2310,2311,2419,2590,2826],"ul",{},[2312,2313,2314,2315,2343,2344,2418],"li",{},"Durch ",[569,2316,2318,2331],{"className":2317},[572],[569,2319,2321],{"className":2320},[576],[578,2322,2323],{"xmlns":580},[582,2324,2325,2329],{},[585,2326,2327],{},[588,2328,690],{},[592,2330,690],{"encoding":594},[569,2332,2334],{"className":2333,"ariaHidden":599},[598],[569,2335,2337,2340],{"className":2336},[603],[569,2338],{"className":2339,"style":608},[607],[569,2341,690],{"className":2342},[612]," teilen vergessen: ",[569,2345,2347,2370],{"className":2346},[572],[569,2348,2350],{"className":2349},[576],[578,2351,2352],{"xmlns":580},[582,2353,2354,2367],{},[585,2355,2356,2358,2360,2362,2364],{},[588,2357,756],{},[790,2359,1327],{},[588,2361,921],{},[790,2363,918],{},[588,2365,2366],{},"10100",[592,2368,2369],{"encoding":594},"100 \\cdot 101 = 10100",[569,2371,2373,2391,2409],{"className":2372,"ariaHidden":599},[598],[569,2374,2376,2379,2382,2385,2388],{"className":2375},[603],[569,2377],{"className":2378,"style":608},[607],[569,2380,756],{"className":2381},[612],[569,2383],{"className":2384,"style":979},[839],[569,2386,1327],{"className":2387},[983],[569,2389],{"className":2390,"style":979},[839],[569,2392,2394,2397,2400,2403,2406],{"className":2393},[603],[569,2395],{"className":2396,"style":608},[607],[569,2398,921],{"className":2399},[612],[569,2401],{"className":2402,"style":999},[839],[569,2404,918],{"className":2405},[1003],[569,2407],{"className":2408,"style":999},[839],[569,2410,2412,2415],{"className":2411},[603],[569,2413],{"className":2414,"style":608},[607],[569,2416,2366],{"className":2417},[612]," ist doppelt so groß wie die Summe.",[2312,2420,2421,2505,2506,2589],{},[569,2422,2424,2450],{"className":2423},[572],[569,2425,2427],{"className":2426},[576],[578,2428,2429],{"xmlns":580},[582,2430,2431,2447],{},[585,2432,2433,2435,2437,2439,2441,2443,2445],{},[627,2434,629],{},[790,2436,1327],{},[790,2438,1331],{"stretchy":1330},[627,2440,629],{},[790,2442,2119],{},[588,2444,590],{},[790,2446,1340],{"stretchy":1330},[592,2448,2449],{"encoding":594},"n \\cdot (n - 1)",[569,2451,2453,2472,2493],{"className":2452,"ariaHidden":599},[598],[569,2454,2456,2460,2463,2466,2469],{"className":2455},[603],[569,2457],{"className":2458,"style":2459},[607],"height:0.4445em;",[569,2461,629],{"className":2462},[612,645],[569,2464],{"className":2465,"style":979},[839],[569,2467,1327],{"className":2468},[983],[569,2470],{"className":2471,"style":979},[839],[569,2473,2475,2478,2481,2484,2487,2490],{"className":2474},[603],[569,2476],{"className":2477,"style":1436},[607],[569,2479,1331],{"className":2480},[1222],[569,2482,629],{"className":2483},[612,645],[569,2485],{"className":2486,"style":979},[839],[569,2488,2119],{"className":2489},[983],[569,2491],{"className":2492,"style":979},[839],[569,2494,2496,2499,2502],{"className":2495},[603],[569,2497],{"className":2498,"style":1436},[607],[569,2500,590],{"className":2501},[612],[569,2503,1340],{"className":2504},[1305]," statt ",[569,2507,2509,2535],{"className":2508},[572],[569,2510,2512],{"className":2511},[576],[578,2513,2514],{"xmlns":580},[582,2515,2516,2532],{},[585,2517,2518,2520,2522,2524,2526,2528,2530],{},[627,2519,629],{},[790,2521,1327],{},[790,2523,1331],{"stretchy":1330},[627,2525,629],{},[790,2527,913],{},[588,2529,590],{},[790,2531,1340],{"stretchy":1330},[592,2533,2534],{"encoding":594},"n \\cdot (n + 1)",[569,2536,2538,2556,2577],{"className":2537,"ariaHidden":599},[598],[569,2539,2541,2544,2547,2550,2553],{"className":2540},[603],[569,2542],{"className":2543,"style":2459},[607],[569,2545,629],{"className":2546},[612,645],[569,2548],{"className":2549,"style":979},[839],[569,2551,1327],{"className":2552},[983],[569,2554],{"className":2555,"style":979},[839],[569,2557,2559,2562,2565,2568,2571,2574],{"className":2558},[603],[569,2560],{"className":2561,"style":1436},[607],[569,2563,1331],{"className":2564},[1222],[569,2566,629],{"className":2567},[612,645],[569,2569],{"className":2570,"style":979},[839],[569,2572,913],{"className":2573},[983],[569,2575],{"className":2576,"style":979},[839],[569,2578,2580,2583,2586],{"className":2579},[603],[569,2581],{"className":2582,"style":1436},[607],[569,2584,590],{"className":2585},[612],[569,2587,1340],{"className":2588},[1305]," rechnen.",[2312,2591,2592,2593,2621,2622,613,2650,2678,2679,2707,2708,2736,2737,2766,2767,2796,2797,2825],{},"Bei Summen, die nicht bei ",[569,2594,2596,2609],{"className":2595},[572],[569,2597,2599],{"className":2598},[576],[578,2600,2601],{"xmlns":580},[582,2602,2603,2607],{},[585,2604,2605],{},[588,2606,590],{},[592,2608,590],{"encoding":594},[569,2610,2612],{"className":2611,"ariaHidden":599},[598],[569,2613,2615,2618],{"className":2614},[603],[569,2616],{"className":2617,"style":608},[607],[569,2619,590],{"className":2620},[612]," beginnen, die falsche Summe abziehen. Für ",[569,2623,2625,2638],{"className":2624},[572],[569,2626,2628],{"className":2627},[576],[578,2629,2630],{"xmlns":580},[582,2631,2632,2636],{},[585,2633,2634],{},[588,2635,955],{},[592,2637,955],{"encoding":594},[569,2639,2641],{"className":2640,"ariaHidden":599},[598],[569,2642,2644,2647],{"className":2643},[603],[569,2645],{"className":2646,"style":608},[607],[569,2648,955],{"className":2649},[612],[569,2651,2653,2666],{"className":2652},[572],[569,2654,2656],{"className":2655},[576],[578,2657,2658],{"xmlns":580},[582,2659,2660,2664],{},[585,2661,2662],{},[588,2663,756],{},[592,2665,756],{"encoding":594},[569,2667,2669],{"className":2668,"ariaHidden":599},[598],[569,2670,2672,2675],{"className":2671},[603],[569,2673],{"className":2674,"style":608},[607],[569,2676,756],{"className":2677},[612]," zieht man die Summe bis ",[569,2680,2682,2695],{"className":2681},[572],[569,2683,2685],{"className":2684},[576],[578,2686,2687],{"xmlns":580},[582,2688,2689,2693],{},[585,2690,2691],{},[588,2692,950],{},[592,2694,950],{"encoding":594},[569,2696,2698],{"className":2697,"ariaHidden":599},[598],[569,2699,2701,2704],{"className":2700},[603],[569,2702],{"className":2703,"style":608},[607],[569,2705,950],{"className":2706},[612]," ab, nicht bis ",[569,2709,2711,2724],{"className":2710},[572],[569,2712,2714],{"className":2713},[576],[578,2715,2716],{"xmlns":580},[582,2717,2718,2722],{},[585,2719,2720],{},[588,2721,955],{},[592,2723,955],{"encoding":594},[569,2725,2727],{"className":2726,"ariaHidden":599},[598],[569,2728,2730,2733],{"className":2729},[603],[569,2731],{"className":2732,"style":608},[607],[569,2734,955],{"className":2735},[612],". Wer nur bis ",[569,2738,2740,2754],{"className":2739},[572],[569,2741,2743],{"className":2742},[576],[578,2744,2745],{"xmlns":580},[582,2746,2747,2752],{},[585,2748,2749],{},[588,2750,2751],{},"49",[592,2753,2751],{"encoding":594},[569,2755,2757],{"className":2756,"ariaHidden":599},[598],[569,2758,2760,2763],{"className":2759},[603],[569,2761],{"className":2762,"style":608},[607],[569,2764,2751],{"className":2765},[612]," abzieht, erhält ",[569,2768,2770,2784],{"className":2769},[572],[569,2771,2773],{"className":2772},[576],[578,2774,2775],{"xmlns":580},[582,2776,2777,2782],{},[585,2778,2779],{},[588,2780,2781],{},"3825",[592,2783,2781],{"encoding":594},[569,2785,2787],{"className":2786,"ariaHidden":599},[598],[569,2788,2790,2793],{"className":2789},[603],[569,2791],{"className":2792,"style":608},[607],[569,2794,2781],{"className":2795},[612],", also ",[569,2798,2800,2813],{"className":2799},[572],[569,2801,2803],{"className":2802},[576],[578,2804,2805],{"xmlns":580},[582,2806,2807,2811],{},[585,2808,2809],{},[588,2810,950],{},[592,2812,950],{"encoding":594},[569,2814,2816],{"className":2815,"ariaHidden":599},[598],[569,2817,2819,2822],{"className":2818},[603],[569,2820],{"className":2821,"style":608},[607],[569,2823,950],{"className":2824},[612]," zu viel.",[2312,2827,2828,2829],{},"Die Formel für Zahlen verwenden, die nicht in Einerschritten aufeinander folgen, z.B. ",[569,2830,2832,2859],{"className":2831},[572],[569,2833,2835],{"className":2834},[576],[578,2836,2837],{"xmlns":580},[582,2838,2839,2856],{},[585,2840,2841,2843,2845,2848,2850,2852,2854],{},[588,2842,690],{},[790,2844,913],{},[588,2846,2847],{},"4",[790,2849,913],{},[588,2851,800],{},[790,2853,913],{},[790,2855,815],{},[592,2857,2858],{"encoding":594},"2 + 4 + 6 + \\ldots",[569,2860,2862,2880,2898,2916],{"className":2861,"ariaHidden":599},[598],[569,2863,2865,2868,2871,2874,2877],{"className":2864},[603],[569,2866],{"className":2867,"style":972},[607],[569,2869,690],{"className":2870},[612],[569,2872],{"className":2873,"style":979},[839],[569,2875,913],{"className":2876},[983],[569,2878],{"className":2879,"style":979},[839],[569,2881,2883,2886,2889,2892,2895],{"className":2882},[603],[569,2884],{"className":2885,"style":972},[607],[569,2887,2847],{"className":2888},[612],[569,2890],{"className":2891,"style":979},[839],[569,2893,913],{"className":2894},[983],[569,2896],{"className":2897,"style":979},[839],[569,2899,2901,2904,2907,2910,2913],{"className":2900},[603],[569,2902],{"className":2903,"style":972},[607],[569,2905,800],{"className":2906},[612],[569,2908],{"className":2909,"style":979},[839],[569,2911,913],{"className":2912},[983],[569,2914],{"className":2915,"style":979},[839],[569,2917,2919,2923],{"className":2918},[603],[569,2920],{"className":2921,"style":2922},[607],"height:0.123em;",[569,2924,815],{"className":2925},[880],{"title":2927,"searchDepth":2928,"depth":2928,"links":2929},"",2,[2930,2931,2932,2933],{"id":562,"depth":2928,"text":563},{"id":887,"depth":2928,"text":888},{"id":1496,"depth":2928,"text":1497},{"id":2306,"depth":2928,"text":2307},[2935,2938,2942,2944,2946,2948,2950,2952,2954,2956],{"lhs":2936,"rhs":2937},"n*(n + 1)\u002F2 + (n + 1)","(n + 1)*(n + 2)\u002F2",{"lhs":2939,"rhs":1605,"where":2940},"n*(n + 1)\u002F2",{"n":2941},100,{"lhs":2943,"rhs":1605},"sum(1:100)",{"lhs":2945,"rhs":1605},"50*101",{"lhs":2947,"rhs":1878},"40*41\u002F2",{"lhs":2949,"rhs":1878},"sum(1:40)",{"lhs":2951,"rhs":2140},"50*51\u002F2",{"lhs":2953,"rhs":2145},"5050 - 1275",{"lhs":2955,"rhs":2145},"sum(51:100)",{"lhs":2957,"rhs":2781},"5050 - 49*50\u002F2","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 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xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmo>+\u003C\u002Fmo>\u003Cmn>3\u003C\u002Fmn>\u003Cmo>+\u003C\u002Fmo>\u003Cmo>…\u003C\u002Fmo>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\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>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">1 + 2 + 3 + \\ldots + n = \\frac{n \\cdot (n + 1)}{2}\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:0.7278em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7278em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7278em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">3\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan 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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\">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>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan 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encoding=\"application\u002Fx-tex\">n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","VETtcpMafzRtKW9so9xaAdofF-LgennXTSF8NJBucjE",[2988,2991,2994],{"stem":2989,"title":2990,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Farithmetische-folge","Arithmetische Folge",{"stem":2992,"title":2993,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fsumme-arithmetische-folge","Summe einer arithmetischen Folge",{"stem":2995,"title":2996,"category":412},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fsumme-der-quadratzahlen","Summe der Quadratzahlen",1793824263984]