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Die Partialsummen nähern sich dann dem festen Wert ",[568,1133,1135,1163],{"className":1134},[571],[568,1136,1138],{"className":1137},[575],[577,1139,1140],{"xmlns":579},[581,1141,1142,1160],{},[584,1143,1144],{},[613,1145,1146,1152],{},[587,1147,1148,1150],{},[590,1149,604],{},[606,1151,608],{},[584,1153,1154,1156,1158],{},[606,1155,608],{},[597,1157,621],{},[590,1159,627],{},[639,1161,1162],{"encoding":641},"\\frac{a_1}{1 - q}",[568,1164,1166],{"className":1165,"ariaHidden":647},[646],[568,1167,1169,1173],{"className":1168},[651],[568,1170],{"className":1171,"style":1172},[655],"height:1.1926em;vertical-align:-0.4811em;",[568,1174,1176,1179,1286],{"className":1175},[660],[568,1177],{"className":1178},[799,800],[568,1180,1182],{"className":1181},[613],[568,1183,1185,1278],{"className":1184},[672,673],[568,1186,1188,1275],{"className":1187},[677],[568,1189,1192,1212,1220],{"className":1190,"style":1191},[681],"height:0.7115em;",[568,1193,1194,1197],{"style":816},[568,1195],{"className":1196,"style":820},[689],[568,1198,1200],{"className":1199},[694,695,696,697],[568,1201,1203,1206,1209],{"className":1202},[660,697],[568,1204,608],{"className":1205},[660,697],[568,1207,621],{"className":1208},[782,697],[568,1210,627],{"className":1211,"style":836},[660,664,697],[568,1213,1214,1217],{"style":839},[568,1215],{"className":1216,"style":820},[689],[568,1218],{"className":1219,"style":847},[846],[568,1221,1223,1226],{"style":1222},"top:-3.4101em;",[568,1224],{"className":1225,"style":820},[689],[568,1227,1229],{"className":1228},[694,695,696,697],[568,1230,1232],{"className":1231},[660,697],[568,1233,1235,1238],{"className":1234},[660,697],[568,1236,604],{"className":1237},[660,664,697],[568,1239,1241],{"className":1240},[668],[568,1242,1244,1266],{"className":1243},[672,673],[568,1245,1247,1263],{"className":1246},[677],[568,1248,1251],{"className":1249,"style":1250},[681],"height:0.3173em;",[568,1252,1254,1257],{"style":1253},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[568,1255],{"className":1256,"style":891},[689],[568,1258,1260],{"className":1259},[694,895,896,697],[568,1261,608],{"className":1262},[660,697],[568,1264,705],{"className":1265},[704],[568,1267,1269],{"className":1268},[677],[568,1270,1273],{"className":1271,"style":1272},[681],"height:0.143em;",[568,1274],{},[568,1276,705],{"className":1277},[704],[568,1279,1281],{"className":1280},[677],[568,1282,1284],{"className":1283,"style":909},[681],[568,1285],{},[568,1287],{"className":1288},[915,800],". Man sagt, die Reihe ",[1291,1292,1293],"strong",{},"konvergiert",", und nennt diesen Grenzwert den ",[1291,1296,1297],{},"Wert"," oder die ",[1291,1300,1301],{},"Summe"," der Reihe.",[564,1304,1305,1306,1368,1369,1503,1504,1532,1533,1536,1537,1687],{},"Für ",[568,1307,1309,1332],{"className":1308},[571],[568,1310,1312],{"className":1311},[575],[577,1313,1314],{"xmlns":579},[581,1315,1316,1329],{},[584,1317,1318,1320,1322,1324,1327],{},[590,1319,932],{"mathvariant":931},[590,1321,627],{},[590,1323,932],{"mathvariant":931},[597,1325,1326],{},"≥",[606,1328,608],{},[639,1330,1331],{"encoding":641},"|q| \\geq 1",[568,1333,1335,1359],{"className":1334,"ariaHidden":647},[646],[568,1336,1338,1341,1344,1347,1350,1353,1356],{"className":1337},[651],[568,1339],{"className":1340,"style":954},[655],[568,1342,932],{"className":1343},[660],[568,1345,627],{"className":1346,"style":836},[660,664],[568,1348,932],{"className":1349},[660],[568,1351],{"className":1352,"style":719},[718],[568,1354,1326],{"className":1355},[723],[568,1357],{"className":1358,"style":719},[718],[568,1360,1362,1365],{"className":1361},[651],[568,1363],{"className":1364,"style":979},[655],[568,1366,608],{"className":1367},[660]," (und ",[568,1370,1372,1395],{"className":1371},[571],[568,1373,1375],{"className":1374},[575],[577,1376,1377],{"xmlns":579},[581,1378,1379,1392],{},[584,1380,1381,1387,1390],{},[587,1382,1383,1385],{},[590,1384,604],{},[606,1386,608],{},[597,1388,1389],{"mathvariant":931},"≠",[606,1391,1116],{},[639,1393,1394],{"encoding":641},"a_1 \\neq 0",[568,1396,1398,1494],{"className":1397,"ariaHidden":647},[646],[568,1399,1401,1405,1445,1448,1491],{"className":1400},[651],[568,1402],{"className":1403,"style":1404},[655],"height:0.8889em;vertical-align:-0.1944em;",[568,1406,1408,1411],{"className":1407},[660],[568,1409,604],{"className":1410},[660,664],[568,1412,1414],{"className":1413},[668],[568,1415,1417,1437],{"className":1416},[672,673],[568,1418,1420,1434],{"className":1419},[677],[568,1421,1423],{"className":1422,"style":752},[681],[568,1424,1425,1428],{"style":685},[568,1426],{"className":1427,"style":690},[689],[568,1429,1431],{"className":1430},[694,695,696,697],[568,1432,608],{"className":1433},[660,697],[568,1435,705],{"className":1436},[704],[568,1438,1440],{"className":1439},[677],[568,1441,1443],{"className":1442,"style":712},[681],[568,1444],{},[568,1446],{"className":1447,"style":719},[718],[568,1449,1451,1484,1488],{"className":1450},[723],[568,1452,1454],{"className":1453},[723],[568,1455,1458],{"className":1456},[660,1457],"vbox",[568,1459,1462],{"className":1460},[1461],"thinbox",[568,1463,1466,1469,1480],{"className":1464},[1465],"rlap",[568,1467],{"className":1468,"style":1404},[655],[568,1470,1473],{"className":1471},[1472],"inner",[568,1474,1476],{"className":1475},[660],[568,1477,1479],{"className":1478},[723],"",[568,1481],{"className":1482},[1483],"fix",[568,1485],{"className":1486},[718,1487],"nobreak",[568,1489,599],{"className":1490},[723],[568,1492],{"className":1493,"style":719},[718],[568,1495,1497,1500],{"className":1496},[651],[568,1498],{"className":1499,"style":979},[655],[568,1501,1116],{"className":1502},[660],") gehen die Glieder nicht gegen ",[568,1505,1507,1520],{"className":1506},[571],[568,1508,1510],{"className":1509},[575],[577,1511,1512],{"xmlns":579},[581,1513,1514,1518],{},[584,1515,1516],{},[606,1517,1116],{},[639,1519,1116],{"encoding":641},[568,1521,1523],{"className":1522,"ariaHidden":647},[646],[568,1524,1526,1529],{"className":1525},[651],[568,1527],{"className":1528,"style":979},[655],[568,1530,1116],{"className":1531},[660],", die Reihe ",[1291,1534,1535],{},"divergiert"," und hat keinen Wert. ",[568,1538,1540,1567],{"className":1539},[571],[568,1541,1543],{"className":1542},[575],[577,1544,1545],{"xmlns":579},[581,1546,1547,1565],{},[584,1548,1549],{},[613,1550,1551,1557],{},[587,1552,1553,1555],{},[590,1554,604],{},[606,1556,608],{},[584,1558,1559,1561,1563],{},[606,1560,608],{},[597,1562,621],{},[590,1564,627],{},[639,1566,1162],{"encoding":641},[568,1568,1570],{"className":1569,"ariaHidden":647},[646],[568,1571,1573,1576],{"className":1572},[651],[568,1574],{"className":1575,"style":1172},[655],[568,1577,1579,1582,1684],{"className":1578},[660],[568,1580],{"className":1581},[799,800],[568,1583,1585],{"className":1584},[613],[568,1586,1588,1676],{"className":1587},[672,673],[568,1589,1591,1673],{"className":1590},[677],[568,1592,1594,1614,1622],{"className":1593,"style":1191},[681],[568,1595,1596,1599],{"style":816},[568,1597],{"className":1598,"style":820},[689],[568,1600,1602],{"className":1601},[694,695,696,697],[568,1603,1605,1608,1611],{"className":1604},[660,697],[568,1606,608],{"className":1607},[660,697],[568,1609,621],{"className":1610},[782,697],[568,1612,627],{"className":1613,"style":836},[660,664,697],[568,1615,1616,1619],{"style":839},[568,1617],{"className":1618,"style":820},[689],[568,1620],{"className":1621,"style":847},[846],[568,1623,1624,1627],{"style":1222},[568,1625],{"className":1626,"style":820},[689],[568,1628,1630],{"className":1629},[694,695,696,697],[568,1631,1633],{"className":1632},[660,697],[568,1634,1636,1639],{"className":1635},[660,697],[568,1637,604],{"className":1638},[660,664,697],[568,1640,1642],{"className":1641},[668],[568,1643,1645,1665],{"className":1644},[672,673],[568,1646,1648,1662],{"className":1647},[677],[568,1649,1651],{"className":1650,"style":1250},[681],[568,1652,1653,1656],{"style":1253},[568,1654],{"className":1655,"style":891},[689],[568,1657,1659],{"className":1658},[694,895,896,697],[568,1660,608],{"className":1661},[660,697],[568,1663,705],{"className":1664},[704],[568,1666,1668],{"className":1667},[677],[568,1669,1671],{"className":1670,"style":1272},[681],[568,1672],{},[568,1674,705],{"className":1675},[704],[568,1677,1679],{"className":1678},[677],[568,1680,1682],{"className":1681,"style":909},[681],[568,1683],{},[568,1685],{"className":1686},[915,800]," darf man dann nicht verwenden.",[564,1689,1690,1691,1719,1720,1908],{},"Der Abstand zwischen Grenzwert und ",[568,1692,1694,1707],{"className":1693},[571],[568,1695,1697],{"className":1696},[575],[577,1698,1699],{"xmlns":579},[581,1700,1701,1705],{},[584,1702,1703],{},[590,1704,595],{},[639,1706,595],{"encoding":641},[568,1708,1710],{"className":1709,"ariaHidden":647},[646],[568,1711,1713,1716],{"className":1712},[651],[568,1714],{"className":1715,"style":1079},[655],[568,1717,595],{"className":1718},[660,664],"-ter Partialsumme ist genau ",[568,1721,1723,1759],{"className":1722},[571],[568,1724,1726],{"className":1725},[575],[577,1727,1728],{"xmlns":579},[581,1729,1730,1756],{},[584,1731,1732],{},[613,1733,1734,1748],{},[584,1735,1736,1742],{},[587,1737,1738,1740],{},[590,1739,604],{},[606,1741,608],{},[623,1743,1744,1746],{},[590,1745,627],{},[590,1747,595],{},[584,1749,1750,1752,1754],{},[606,1751,608],{},[597,1753,621],{},[590,1755,627],{},[639,1757,1758],{"encoding":641},"\\frac{a_1 q^n}{1 - q}",[568,1760,1762],{"className":1761,"ariaHidden":647},[646],[568,1763,1765,1768],{"className":1764},[651],[568,1766],{"className":1767,"style":792},[655],[568,1769,1771,1774,1905],{"className":1770},[660],[568,1772],{"className":1773},[799,800],[568,1775,1777],{"className":1776},[613],[568,1778,1780,1897],{"className":1779},[672,673],[568,1781,1783,1894],{"className":1782},[677],[568,1784,1786,1806,1814],{"className":1785,"style":813},[681],[568,1787,1788,1791],{"style":816},[568,1789],{"className":1790,"style":820},[689],[568,1792,1794],{"className":1793},[694,695,696,697],[568,1795,1797,1800,1803],{"className":1796},[660,697],[568,1798,608],{"className":1799},[660,697],[568,1801,621],{"className":1802},[782,697],[568,1804,627],{"className":1805,"style":836},[660,664,697],[568,1807,1808,1811],{"style":839},[568,1809],{"className":1810,"style":820},[689],[568,1812],{"className":1813,"style":847},[846],[568,1815,1816,1819],{"style":850},[568,1817],{"className":1818,"style":820},[689],[568,1820,1822],{"className":1821},[694,695,696,697],[568,1823,1825,1865],{"className":1824},[660,697],[568,1826,1828,1831],{"className":1827},[660,697],[568,1829,604],{"className":1830},[660,664,697],[568,1832,1834],{"className":1833},[668],[568,1835,1837,1857],{"className":1836},[672,673],[568,1838,1840,1854],{"className":1839},[677],[568,1841,1843],{"className":1842,"style":1250},[681],[568,1844,1845,1848],{"style":1253},[568,1846],{"className":1847,"style":891},[689],[568,1849,1851],{"className":1850},[694,895,896,697],[568,1852,608],{"className":1853},[660,697],[568,1855,705],{"className":1856},[704],[568,1858,1860],{"className":1859},[677],[568,1861,1863],{"className":1862,"style":1272},[681],[568,1864],{},[568,1866,1868,1871],{"className":1867},[660,697],[568,1869,627],{"className":1870,"style":836},[660,664,697],[568,1872,1874],{"className":1873},[668],[568,1875,1877],{"className":1876},[672],[568,1878,1880],{"className":1879},[677],[568,1881,1883],{"className":1882,"style":884},[681],[568,1884,1885,1888],{"style":887},[568,1886],{"className":1887,"style":891},[689],[568,1889,1891],{"className":1890},[694,895,896,697],[568,1892,595],{"className":1893},[660,664,697],[568,1895,705],{"className":1896},[704],[568,1898,1900],{"className":1899},[677],[568,1901,1903],{"className":1902,"style":909},[681],[568,1904],{},[568,1906],{"className":1907},[915,800],". Damit lässt sich abschätzen, wie viele Glieder für eine bestimmte Genauigkeit nötig sind.",[559,1910,1912],{"id":1911},"beispiele","Beispiele",[564,1914,1915],{},"Halbiert man immer weiter, ergibt die Summe genau ein Ganzes:",[568,1917,1920],{"className":1918},[1919],"katex-display",[568,1921,1923,1986],{"className":1922},[571],[568,1924,1926],{"className":1925},[575],[577,1927,1929],{"xmlns":579,"display":1928},"block",[581,1930,1931,1983],{},[584,1932,1933,1940,1943,1950,1952,1959,1961,1964,1966,1979,1981],{},[613,1934,1935,1937],{},[606,1936,608],{},[606,1938,1939],{},"2",[597,1941,1942],{},"+",[613,1944,1945,1947],{},[606,1946,608],{},[606,1948,1949],{},"4",[597,1951,1942],{},[613,1953,1954,1956],{},[606,1955,608],{},[606,1957,1958],{},"8",[597,1960,1942],{},[597,1962,1963],{},"…",[597,1965,599],{},[613,1967,1968,1971],{},[606,1969,1970],{},"0,5",[584,1972,1973,1975,1977],{},[606,1974,608],{},[597,1976,621],{},[606,1978,1970],{},[597,1980,599],{},[606,1982,608],{},[639,1984,1985],{"encoding":641},"\\frac{1}{2} + \\frac{1}{4} + \\frac{1}{8} + \\ldots = \\frac{0{,}5}{1 - 0{,}5} = 1",[568,1987,1989,2071,2148,2225,2245,2357],{"className":1988,"ariaHidden":647},[646],[568,1990,1992,1996,2062,2065,2068],{"className":1991},[651],[568,1993],{"className":1994,"style":1995},[655],"height:2.0074em;vertical-align:-0.686em;",[568,1997,1999,2002,2059],{"className":1998},[660],[568,2000],{"className":2001},[799,800],[568,2003,2005],{"className":2004},[613],[568,2006,2008,2050],{"className":2007},[672,673],[568,2009,2011,2047],{"className":2010},[677],[568,2012,2015,2027,2035],{"className":2013,"style":2014},[681],"height:1.3214em;",[568,2016,2018,2021],{"style":2017},"top:-2.314em;",[568,2019],{"className":2020,"style":820},[689],[568,2022,2024],{"className":2023},[660],[568,2025,1939],{"className":2026},[660],[568,2028,2029,2032],{"style":839},[568,2030],{"className":2031,"style":820},[689],[568,2033],{"className":2034,"style":847},[846],[568,2036,2038,2041],{"style":2037},"top:-3.677em;",[568,2039],{"className":2040,"style":820},[689],[568,2042,2044],{"className":2043},[660],[568,2045,608],{"className":2046},[660],[568,2048,705],{"className":2049},[704],[568,2051,2053],{"className":2052},[677],[568,2054,2057],{"className":2055,"style":2056},[681],"height:0.686em;",[568,2058],{},[568,2060],{"className":2061},[915,800],[568,2063],{"className":2064,"style":778},[718],[568,2066,1942],{"className":2067},[782],[568,2069],{"className":2070,"style":778},[718],[568,2072,2074,2077,2139,2142,2145],{"className":2073},[651],[568,2075],{"className":2076,"style":1995},[655],[568,2078,2080,2083,2136],{"className":2079},[660],[568,2081],{"className":2082},[799,800],[568,2084,2086],{"className":2085},[613],[568,2087,2089,2128],{"className":2088},[672,673],[568,2090,2092,2125],{"className":2091},[677],[568,2093,2095,2106,2114],{"className":2094,"style":2014},[681],[568,2096,2097,2100],{"style":2017},[568,2098],{"className":2099,"style":820},[689],[568,2101,2103],{"className":2102},[660],[568,2104,1949],{"className":2105},[660],[568,2107,2108,2111],{"style":839},[568,2109],{"className":2110,"style":820},[689],[568,2112],{"className":2113,"style":847},[846],[568,2115,2116,2119],{"style":2037},[568,2117],{"className":2118,"style":820},[689],[568,2120,2122],{"className":2121},[660],[568,2123,608],{"className":2124},[660],[568,2126,705],{"className":2127},[704],[568,2129,2131],{"className":2130},[677],[568,2132,2134],{"className":2133,"style":2056},[681],[568,2135],{},[568,2137],{"className":2138},[915,800],[568,2140],{"className":2141,"style":778},[718],[568,2143,1942],{"className":2144},[782],[568,2146],{"className":2147,"style":778},[718],[568,2149,2151,2154,2216,2219,2222],{"className":2150},[651],[568,2152],{"className":2153,"style":1995},[655],[568,2155,2157,2160,2213],{"className":2156},[660],[568,2158],{"className":2159},[799,800],[568,2161,2163],{"className":2162},[613],[568,2164,2166,2205],{"className":2165},[672,673],[568,2167,2169,2202],{"className":2168},[677],[568,2170,2172,2183,2191],{"className":2171,"style":2014},[681],[568,2173,2174,2177],{"style":2017},[568,2175],{"className":2176,"style":820},[689],[568,2178,2180],{"className":2179},[660],[568,2181,1958],{"className":2182},[660],[568,2184,2185,2188],{"style":839},[568,2186],{"className":2187,"style":820},[689],[568,2189],{"className":2190,"style":847},[846],[568,2192,2193,2196],{"style":2037},[568,2194],{"className":2195,"style":820},[689],[568,2197,2199],{"className":2198},[660],[568,2200,608],{"className":2201},[660],[568,2203,705],{"className":2204},[704],[568,2206,2208],{"className":2207},[677],[568,2209,2211],{"className":2210,"style":2056},[681],[568,2212],{},[568,2214],{"className":2215},[915,800],[568,2217],{"className":2218,"style":778},[718],[568,2220,1942],{"className":2221},[782],[568,2223],{"className":2224,"style":778},[718],[568,2226,2228,2232,2236,2239,2242],{"className":2227},[651],[568,2229],{"className":2230,"style":2231},[655],"height:0.3669em;",[568,2233,1963],{"className":2234},[2235],"minner",[568,2237],{"className":2238,"style":719},[718],[568,2240,599],{"className":2241},[723],[568,2243],{"className":2244,"style":719},[718],[568,2246,2248,2252,2348,2351,2354],{"className":2247},[651],[568,2249],{"className":2250,"style":2251},[655],"height:2.2019em;vertical-align:-0.8804em;",[568,2253,2255,2258,2345],{"className":2254},[660],[568,2256],{"className":2257},[799,800],[568,2259,2261],{"className":2260},[613],[568,2262,2264,2336],{"className":2263},[672,673],[568,2265,2267,2333],{"className":2266},[677],[568,2268,2270,2305,2313],{"className":2269,"style":2014},[681],[568,2271,2272,2275],{"style":2017},[568,2273],{"className":2274,"style":820},[689],[568,2276,2278,2281,2284,2287,2290,2293,2301],{"className":2277},[660],[568,2279,608],{"className":2280},[660],[568,2282],{"className":2283,"style":778},[718],[568,2285,621],{"className":2286},[782],[568,2288],{"className":2289,"style":778},[718],[568,2291,1116],{"className":2292},[660],[568,2294,2296],{"className":2295},[660],[568,2297,2300],{"className":2298},[2299],"mpunct",",",[568,2302,2304],{"className":2303},[660],"5",[568,2306,2307,2310],{"style":839},[568,2308],{"className":2309,"style":820},[689],[568,2311],{"className":2312,"style":847},[846],[568,2314,2315,2318],{"style":2037},[568,2316],{"className":2317,"style":820},[689],[568,2319,2321,2324,2330],{"className":2320},[660],[568,2322,1116],{"className":2323},[660],[568,2325,2327],{"className":2326},[660],[568,2328,2300],{"className":2329},[2299],[568,2331,2304],{"className":2332},[660],[568,2334,705],{"className":2335},[704],[568,2337,2339],{"className":2338},[677],[568,2340,2343],{"className":2341,"style":2342},[681],"height:0.8804em;",[568,2344],{},[568,2346],{"className":2347},[915,800],[568,2349],{"className":2350,"style":719},[718],[568,2352,599],{"className":2353},[723],[568,2355],{"className":2356,"style":719},[718],[568,2358,2360,2363],{"className":2359},[651],[568,2361],{"className":2362,"style":979},[655],[568,2364,608],{"className":2365},[660],[564,2367,2368,2369,2451,2452,2581,2582,2683,2684,2746],{},"Die periodische Dezimalzahl ",[568,2370,2372,2396],{"className":2371},[571],[568,2373,2375],{"className":2374},[575],[577,2376,2377],{"xmlns":579},[581,2378,2379,2393],{},[584,2380,2381,2384],{},[606,2382,2383],{},"0,",[2385,2386,2387,2390],"mover",{"accent":647},[606,2388,2389],{},"9",[597,2391,2392],{"stretchy":647},"‾",[639,2394,2395],{"encoding":641},"0{,}\\overline{9}",[568,2397,2399],{"className":2398,"ariaHidden":647},[646],[568,2400,2402,2406,2409,2415],{"className":2401},[651],[568,2403],{"className":2404,"style":2405},[655],"height:1.0389em;vertical-align:-0.1944em;",[568,2407,1116],{"className":2408},[660],[568,2410,2412],{"className":2411},[660],[568,2413,2300],{"className":2414},[2299],[568,2416,2419],{"className":2417},[660,2418],"overline",[568,2420,2422],{"className":2421},[672],[568,2423,2425],{"className":2424},[677],[568,2426,2429,2441],{"className":2427,"style":2428},[681],"height:0.8444em;",[568,2430,2432,2435],{"style":2431},"top:-3em;",[568,2433],{"className":2434,"style":820},[689],[568,2436,2438],{"className":2437},[660],[568,2439,2389],{"className":2440},[660],[568,2442,2444,2447],{"style":2443},"top:-3.7644em;",[568,2445],{"className":2446,"style":820},[689],[568,2448],{"className":2449,"style":847},[2450],"overline-line"," ist die Reihe ",[568,2453,2455,2484],{"className":2454},[571],[568,2456,2458],{"className":2457},[575],[577,2459,2460],{"xmlns":579},[581,2461,2462,2481],{},[584,2463,2464,2467,2469,2472,2474,2477,2479],{},[606,2465,2466],{},"0,9",[597,2468,1942],{},[606,2470,2471],{},"0,09",[597,2473,1942],{},[606,2475,2476],{},"0,009",[597,2478,1942],{},[597,2480,1963],{},[639,2482,2483],{"encoding":641},"0{,}9 + 0{,}09 + 0{,}009 + \\ldots",[568,2485,2487,2515,2543,2571],{"className":2486,"ariaHidden":647},[646],[568,2488,2490,2494,2497,2503,2506,2509,2512],{"className":2489},[651],[568,2491],{"className":2492,"style":2493},[655],"height:0.8389em;vertical-align:-0.1944em;",[568,2495,1116],{"className":2496},[660],[568,2498,2500],{"className":2499},[660],[568,2501,2300],{"className":2502},[2299],[568,2504,2389],{"className":2505},[660],[568,2507],{"className":2508,"style":778},[718],[568,2510,1942],{"className":2511},[782],[568,2513],{"className":2514,"style":778},[718],[568,2516,2518,2521,2524,2530,2534,2537,2540],{"className":2517},[651],[568,2519],{"className":2520,"style":2493},[655],[568,2522,1116],{"className":2523},[660],[568,2525,2527],{"className":2526},[660],[568,2528,2300],{"className":2529},[2299],[568,2531,2533],{"className":2532},[660],"09",[568,2535],{"className":2536,"style":778},[718],[568,2538,1942],{"className":2539},[782],[568,2541],{"className":2542,"style":778},[718],[568,2544,2546,2549,2552,2558,2562,2565,2568],{"className":2545},[651],[568,2547],{"className":2548,"style":2493},[655],[568,2550,1116],{"className":2551},[660],[568,2553,2555],{"className":2554},[660],[568,2556,2300],{"className":2557},[2299],[568,2559,2561],{"className":2560},[660],"009",[568,2563],{"className":2564,"style":778},[718],[568,2566,1942],{"className":2567},[782],[568,2569],{"className":2570,"style":778},[718],[568,2572,2574,2578],{"className":2573},[651],[568,2575],{"className":2576,"style":2577},[655],"height:0.123em;",[568,2579,1963],{"className":2580},[2235]," mit ",[568,2583,2585,2607],{"className":2584},[571],[568,2586,2588],{"className":2587},[575],[577,2589,2590],{"xmlns":579},[581,2591,2592,2604],{},[584,2593,2594,2600,2602],{},[587,2595,2596,2598],{},[590,2597,604],{},[606,2599,608],{},[597,2601,599],{},[606,2603,2466],{},[639,2605,2606],{"encoding":641},"a_1 = 0{,}9",[568,2608,2610,2665],{"className":2609,"ariaHidden":647},[646],[568,2611,2613,2616,2656,2659,2662],{"className":2612},[651],[568,2614],{"className":2615,"style":656},[655],[568,2617,2619,2622],{"className":2618},[660],[568,2620,604],{"className":2621},[660,664],[568,2623,2625],{"className":2624},[668],[568,2626,2628,2648],{"className":2627},[672,673],[568,2629,2631,2645],{"className":2630},[677],[568,2632,2634],{"className":2633,"style":752},[681],[568,2635,2636,2639],{"style":685},[568,2637],{"className":2638,"style":690},[689],[568,2640,2642],{"className":2641},[694,695,696,697],[568,2643,608],{"className":2644},[660,697],[568,2646,705],{"className":2647},[704],[568,2649,2651],{"className":2650},[677],[568,2652,2654],{"className":2653,"style":712},[681],[568,2655],{},[568,2657],{"className":2658,"style":719},[718],[568,2660,599],{"className":2661},[723],[568,2663],{"className":2664,"style":719},[718],[568,2666,2668,2671,2674,2680],{"className":2667},[651],[568,2669],{"className":2670,"style":2493},[655],[568,2672,1116],{"className":2673},[660],[568,2675,2677],{"className":2676},[660],[568,2678,2300],{"className":2679},[2299],[568,2681,2389],{"className":2682},[660]," und ",[568,2685,2687,2706],{"className":2686},[571],[568,2688,2690],{"className":2689},[575],[577,2691,2692],{"xmlns":579},[581,2693,2694,2703],{},[584,2695,2696,2698,2700],{},[590,2697,627],{},[597,2699,599],{},[606,2701,2702],{},"0,1",[639,2704,2705],{"encoding":641},"q = 0{,}1",[568,2707,2709,2728],{"className":2708,"ariaHidden":647},[646],[568,2710,2712,2716,2719,2722,2725],{"className":2711},[651],[568,2713],{"className":2714,"style":2715},[655],"height:0.625em;vertical-align:-0.1944em;",[568,2717,627],{"className":2718,"style":836},[660,664],[568,2720],{"className":2721,"style":719},[718],[568,2723,599],{"className":2724},[723],[568,2726],{"className":2727,"style":719},[718],[568,2729,2731,2734,2737,2743],{"className":2730},[651],[568,2732],{"className":2733,"style":2493},[655],[568,2735,1116],{"className":2736},[660],[568,2738,2740],{"className":2739},[660],[568,2741,2300],{"className":2742},[2299],[568,2744,608],{"className":2745},[660],":",[568,2748,2750],{"className":2749},[1919],[568,2751,2753,2791],{"className":2752},[571],[568,2754,2756],{"className":2755},[575],[577,2757,2758],{"xmlns":579,"display":1928},[581,2759,2760,2788],{},[584,2761,2762,2764,2770,2772,2784,2786],{},[606,2763,2383],{},[2385,2765,2766,2768],{"accent":647},[606,2767,2389],{},[597,2769,2392],{"stretchy":647},[597,2771,599],{},[613,2773,2774,2776],{},[606,2775,2466],{},[584,2777,2778,2780,2782],{},[606,2779,608],{},[597,2781,621],{},[606,2783,2702],{},[597,2785,599],{},[606,2787,608],{},[639,2789,2790],{"encoding":641},"0{,}\\overline{9} = \\frac{0{,}9}{1 - 0{,}1} = 1",[568,2792,2794,2849,2956],{"className":2793,"ariaHidden":647},[646],[568,2795,2797,2800,2803,2809,2840,2843,2846],{"className":2796},[651],[568,2798],{"className":2799,"style":2405},[655],[568,2801,1116],{"className":2802},[660],[568,2804,2806],{"className":2805},[660],[568,2807,2300],{"className":2808},[2299],[568,2810,2812],{"className":2811},[660,2418],[568,2813,2815],{"className":2814},[672],[568,2816,2818],{"className":2817},[677],[568,2819,2821,2832],{"className":2820,"style":2428},[681],[568,2822,2823,2826],{"style":2431},[568,2824],{"className":2825,"style":820},[689],[568,2827,2829],{"className":2828},[660],[568,2830,2389],{"className":2831},[660],[568,2833,2834,2837],{"style":2443},[568,2835],{"className":2836,"style":820},[689],[568,2838],{"className":2839,"style":847},[2450],[568,2841],{"className":2842,"style":719},[718],[568,2844,599],{"className":2845},[723],[568,2847],{"className":2848,"style":719},[718],[568,2850,2852,2855,2947,2950,2953],{"className":2851},[651],[568,2853],{"className":2854,"style":2251},[655],[568,2856,2858,2861,2944],{"className":2857},[660],[568,2859],{"className":2860},[799,800],[568,2862,2864],{"className":2863},[613],[568,2865,2867,2936],{"className":2866},[672,673],[568,2868,2870,2933],{"className":2869},[677],[568,2871,2873,2905,2913],{"className":2872,"style":2014},[681],[568,2874,2875,2878],{"style":2017},[568,2876],{"className":2877,"style":820},[689],[568,2879,2881,2884,2887,2890,2893,2896,2902],{"className":2880},[660],[568,2882,608],{"className":2883},[660],[568,2885],{"className":2886,"style":778},[718],[568,2888,621],{"className":2889},[782],[568,2891],{"className":2892,"style":778},[718],[568,2894,1116],{"className":2895},[660],[568,2897,2899],{"className":2898},[660],[568,2900,2300],{"className":2901},[2299],[568,2903,608],{"className":2904},[660],[568,2906,2907,2910],{"style":839},[568,2908],{"className":2909,"style":820},[689],[568,2911],{"className":2912,"style":847},[846],[568,2914,2915,2918],{"style":2037},[568,2916],{"className":2917,"style":820},[689],[568,2919,2921,2924,2930],{"className":2920},[660],[568,2922,1116],{"className":2923},[660],[568,2925,2927],{"className":2926},[660],[568,2928,2300],{"className":2929},[2299],[568,2931,2389],{"className":2932},[660],[568,2934,705],{"className":2935},[704],[568,2937,2939],{"className":2938},[677],[568,2940,2942],{"className":2941,"style":2342},[681],[568,2943],{},[568,2945],{"className":2946},[915,800],[568,2948],{"className":2949,"style":719},[718],[568,2951,599],{"className":2952},[723],[568,2954],{"className":2955,"style":719},[718],[568,2957,2959,2962],{"className":2958},[651],[568,2960],{"className":2961,"style":979},[655],[568,2963,608],{"className":2964},[660],[564,2966,2967,2968,2581,3041,2683,3143,2746],{},"Genauso wandelt man jede periodische Dezimalzahl in einen Bruch um, z.B. ",[568,2969,2971,2992],{"className":2970},[571],[568,2972,2974],{"className":2973},[575],[577,2975,2976],{"xmlns":579},[581,2977,2978,2989],{},[584,2979,2980,2982],{},[606,2981,2383],{},[2385,2983,2984,2987],{"accent":647},[606,2985,2986],{},"36",[597,2988,2392],{"stretchy":647},[639,2990,2991],{"encoding":641},"0{,}\\overline{36}",[568,2993,2995],{"className":2994,"ariaHidden":647},[646],[568,2996,2998,3001,3004,3010],{"className":2997},[651],[568,2999],{"className":3000,"style":2405},[655],[568,3002,1116],{"className":3003},[660],[568,3005,3007],{"className":3006},[660],[568,3008,2300],{"className":3009},[2299],[568,3011,3013],{"className":3012},[660,2418],[568,3014,3016],{"className":3015},[672],[568,3017,3019],{"className":3018},[677],[568,3020,3022,3033],{"className":3021,"style":2428},[681],[568,3023,3024,3027],{"style":2431},[568,3025],{"className":3026,"style":820},[689],[568,3028,3030],{"className":3029},[660],[568,3031,2986],{"className":3032},[660],[568,3034,3035,3038],{"style":2443},[568,3036],{"className":3037,"style":820},[689],[568,3039],{"className":3040,"style":847},[2450],[568,3042,3044,3067],{"className":3043},[571],[568,3045,3047],{"className":3046},[575],[577,3048,3049],{"xmlns":579},[581,3050,3051,3064],{},[584,3052,3053,3059,3061],{},[587,3054,3055,3057],{},[590,3056,604],{},[606,3058,608],{},[597,3060,599],{},[606,3062,3063],{},"0,36",[639,3065,3066],{"encoding":641},"a_1 = 0{,}36",[568,3068,3070,3125],{"className":3069,"ariaHidden":647},[646],[568,3071,3073,3076,3116,3119,3122],{"className":3072},[651],[568,3074],{"className":3075,"style":656},[655],[568,3077,3079,3082],{"className":3078},[660],[568,3080,604],{"className":3081},[660,664],[568,3083,3085],{"className":3084},[668],[568,3086,3088,3108],{"className":3087},[672,673],[568,3089,3091,3105],{"className":3090},[677],[568,3092,3094],{"className":3093,"style":752},[681],[568,3095,3096,3099],{"style":685},[568,3097],{"className":3098,"style":690},[689],[568,3100,3102],{"className":3101},[694,695,696,697],[568,3103,608],{"className":3104},[660,697],[568,3106,705],{"className":3107},[704],[568,3109,3111],{"className":3110},[677],[568,3112,3114],{"className":3113,"style":712},[681],[568,3115],{},[568,3117],{"className":3118,"style":719},[718],[568,3120,599],{"className":3121},[723],[568,3123],{"className":3124,"style":719},[718],[568,3126,3128,3131,3134,3140],{"className":3127},[651],[568,3129],{"className":3130,"style":2493},[655],[568,3132,1116],{"className":3133},[660],[568,3135,3137],{"className":3136},[660],[568,3138,2300],{"className":3139},[2299],[568,3141,2986],{"className":3142},[660],[568,3144,3146,3165],{"className":3145},[571],[568,3147,3149],{"className":3148},[575],[577,3150,3151],{"xmlns":579},[581,3152,3153,3162],{},[584,3154,3155,3157,3159],{},[590,3156,627],{},[597,3158,599],{},[606,3160,3161],{},"0,01",[639,3163,3164],{"encoding":641},"q = 0{,}01",[568,3166,3168,3186],{"className":3167,"ariaHidden":647},[646],[568,3169,3171,3174,3177,3180,3183],{"className":3170},[651],[568,3172],{"className":3173,"style":2715},[655],[568,3175,627],{"className":3176,"style":836},[660,664],[568,3178],{"className":3179,"style":719},[718],[568,3181,599],{"className":3182},[723],[568,3184],{"className":3185,"style":719},[718],[568,3187,3189,3192,3195,3201],{"className":3188},[651],[568,3190],{"className":3191,"style":2493},[655],[568,3193,1116],{"className":3194},[660],[568,3196,3198],{"className":3197},[660],[568,3199,2300],{"className":3200},[2299],[568,3202,3204],{"className":3203},[660],"01",[568,3206,3208],{"className":3207},[1919],[568,3209,3211,3258],{"className":3210},[571],[568,3212,3214],{"className":3213},[575],[577,3215,3216],{"xmlns":579,"display":1928},[581,3217,3218,3255],{},[584,3219,3220,3222,3228,3230,3237,3239,3246,3248],{},[606,3221,2383],{},[2385,3223,3224,3226],{"accent":647},[606,3225,2986],{},[597,3227,2392],{"stretchy":647},[597,3229,599],{},[613,3231,3232,3234],{},[606,3233,3063],{},[606,3235,3236],{},"0,99",[597,3238,599],{},[613,3240,3241,3243],{},[606,3242,2986],{},[606,3244,3245],{},"99",[597,3247,599],{},[613,3249,3250,3252],{},[606,3251,1949],{},[606,3253,3254],{},"11",[639,3256,3257],{"encoding":641},"0{,}\\overline{36} = \\frac{0{,}36}{0{,}99} = \\frac{36}{99} = \\frac{4}{11}",[568,3259,3261,3316,3411,3488],{"className":3260,"ariaHidden":647},[646],[568,3262,3264,3267,3270,3276,3307,3310,3313],{"className":3263},[651],[568,3265],{"className":3266,"style":2405},[655],[568,3268,1116],{"className":3269},[660],[568,3271,3273],{"className":3272},[660],[568,3274,2300],{"className":3275},[2299],[568,3277,3279],{"className":3278},[660,2418],[568,3280,3282],{"className":3281},[672],[568,3283,3285],{"className":3284},[677],[568,3286,3288,3299],{"className":3287,"style":2428},[681],[568,3289,3290,3293],{"style":2431},[568,3291],{"className":3292,"style":820},[689],[568,3294,3296],{"className":3295},[660],[568,3297,2986],{"className":3298},[660],[568,3300,3301,3304],{"style":2443},[568,3302],{"className":3303,"style":820},[689],[568,3305],{"className":3306,"style":847},[2450],[568,3308],{"className":3309,"style":719},[718],[568,3311,599],{"className":3312},[723],[568,3314],{"className":3315,"style":719},[718],[568,3317,3319,3322,3402,3405,3408],{"className":3318},[651],[568,3320],{"className":3321,"style":2251},[655],[568,3323,3325,3328,3399],{"className":3324},[660],[568,3326],{"className":3327},[799,800],[568,3329,3331],{"className":3330},[613],[568,3332,3334,3391],{"className":3333},[672,673],[568,3335,3337,3388],{"className":3336},[677],[568,3338,3340,3360,3368],{"className":3339,"style":2014},[681],[568,3341,3342,3345],{"style":2017},[568,3343],{"className":3344,"style":820},[689],[568,3346,3348,3351,3357],{"className":3347},[660],[568,3349,1116],{"className":3350},[660],[568,3352,3354],{"className":3353},[660],[568,3355,2300],{"className":3356},[2299],[568,3358,3245],{"className":3359},[660],[568,3361,3362,3365],{"style":839},[568,3363],{"className":3364,"style":820},[689],[568,3366],{"className":3367,"style":847},[846],[568,3369,3370,3373],{"style":2037},[568,3371],{"className":3372,"style":820},[689],[568,3374,3376,3379,3385],{"className":3375},[660],[568,3377,1116],{"className":3378},[660],[568,3380,3382],{"className":3381},[660],[568,3383,2300],{"className":3384},[2299],[568,3386,2986],{"className":3387},[660],[568,3389,705],{"className":3390},[704],[568,3392,3394],{"className":3393},[677],[568,3395,3397],{"className":3396,"style":2342},[681],[568,3398],{},[568,3400],{"className":3401},[915,800],[568,3403],{"className":3404,"style":719},[718],[568,3406,599],{"className":3407},[723],[568,3409],{"className":3410,"style":719},[718],[568,3412,3414,3417,3479,3482,3485],{"className":3413},[651],[568,3415],{"className":3416,"style":1995},[655],[568,3418,3420,3423,3476],{"className":3419},[660],[568,3421],{"className":3422},[799,800],[568,3424,3426],{"className":3425},[613],[568,3427,3429,3468],{"className":3428},[672,673],[568,3430,3432,3465],{"className":3431},[677],[568,3433,3435,3446,3454],{"className":3434,"style":2014},[681],[568,3436,3437,3440],{"style":2017},[568,3438],{"className":3439,"style":820},[689],[568,3441,3443],{"className":3442},[660],[568,3444,3245],{"className":3445},[660],[568,3447,3448,3451],{"style":839},[568,3449],{"className":3450,"style":820},[689],[568,3452],{"className":3453,"style":847},[846],[568,3455,3456,3459],{"style":2037},[568,3457],{"className":3458,"style":820},[689],[568,3460,3462],{"className":3461},[660],[568,3463,2986],{"className":3464},[660],[568,3466,705],{"className":3467},[704],[568,3469,3471],{"className":3470},[677],[568,3472,3474],{"className":3473,"style":2056},[681],[568,3475],{},[568,3477],{"className":3478},[915,800],[568,3480],{"className":3481,"style":719},[718],[568,3483,599],{"className":3484},[723],[568,3486],{"className":3487,"style":719},[718],[568,3489,3491,3494],{"className":3490},[651],[568,3492],{"className":3493,"style":1995},[655],[568,3495,3497,3500,3553],{"className":3496},[660],[568,3498],{"className":3499},[799,800],[568,3501,3503],{"className":3502},[613],[568,3504,3506,3545],{"className":3505},[672,673],[568,3507,3509,3542],{"className":3508},[677],[568,3510,3512,3523,3531],{"className":3511,"style":2014},[681],[568,3513,3514,3517],{"style":2017},[568,3515],{"className":3516,"style":820},[689],[568,3518,3520],{"className":3519},[660],[568,3521,3254],{"className":3522},[660],[568,3524,3525,3528],{"style":839},[568,3526],{"className":3527,"style":820},[689],[568,3529],{"className":3530,"style":847},[846],[568,3532,3533,3536],{"style":2037},[568,3534],{"className":3535,"style":820},[689],[568,3537,3539],{"className":3538},[660],[568,3540,1949],{"className":3541},[660],[568,3543,705],{"className":3544},[704],[568,3546,3548],{"className":3547},[677],[568,3549,3551],{"className":3550,"style":2056},[681],[568,3552],{},[568,3554],{"className":3555},[915,800],[564,3557,3558,3559,3688],{},"Mit negativem Quotienten ",[568,3560,3562,3586],{"className":3561},[571],[568,3563,3565],{"className":3564},[575],[577,3566,3567],{"xmlns":579},[581,3568,3569,3583],{},[584,3570,3571,3573,3575,3577],{},[590,3572,627],{},[597,3574,599],{},[597,3576,621],{},[613,3578,3579,3581],{},[606,3580,608],{},[606,3582,1939],{},[639,3584,3585],{"encoding":641},"q = -\\frac{1}{2}",[568,3587,3589,3607],{"className":3588,"ariaHidden":647},[646],[568,3590,3592,3595,3598,3601,3604],{"className":3591},[651],[568,3593],{"className":3594,"style":2715},[655],[568,3596,627],{"className":3597,"style":836},[660,664],[568,3599],{"className":3600,"style":719},[718],[568,3602,599],{"className":3603},[723],[568,3605],{"className":3606,"style":719},[718],[568,3608,3610,3614,3617],{"className":3609},[651],[568,3611],{"className":3612,"style":3613},[655],"height:1.1901em;vertical-align:-0.345em;",[568,3615,621],{"className":3616},[660],[568,3618,3620,3623,3685],{"className":3619},[660],[568,3621],{"className":3622},[799,800],[568,3624,3626],{"className":3625},[613],[568,3627,3629,3676],{"className":3628},[672,673],[568,3630,3632,3673],{"className":3631},[677],[568,3633,3636,3650,3658],{"className":3634,"style":3635},[681],"height:0.8451em;",[568,3637,3638,3641],{"style":816},[568,3639],{"className":3640,"style":820},[689],[568,3642,3644],{"className":3643},[694,695,696,697],[568,3645,3647],{"className":3646},[660,697],[568,3648,1939],{"className":3649},[660,697],[568,3651,3652,3655],{"style":839},[568,3653],{"className":3654,"style":820},[689],[568,3656],{"className":3657,"style":847},[846],[568,3659,3661,3664],{"style":3660},"top:-3.394em;",[568,3662],{"className":3663,"style":820},[689],[568,3665,3667],{"className":3666},[694,695,696,697],[568,3668,3670],{"className":3669},[660,697],[568,3671,608],{"className":3672},[660,697],[568,3674,705],{"className":3675},[704],[568,3677,3679],{"className":3678},[677],[568,3680,3683],{"className":3681,"style":3682},[681],"height:0.345em;",[568,3684],{},[568,3686],{"className":3687},[915,800]," springen die Partialsummen hin und her, konvergieren aber trotzdem:",[568,3690,3692],{"className":3691},[1919],[568,3693,3695,3764],{"className":3694},[571],[568,3696,3698],{"className":3697},[575],[577,3699,3700],{"xmlns":579,"display":1928},[581,3701,3702,3761],{},[584,3703,3704,3706,3708,3714,3716,3722,3724,3730,3732,3734,3736,3752,3754],{},[606,3705,608],{},[597,3707,621],{},[613,3709,3710,3712],{},[606,3711,608],{},[606,3713,1939],{},[597,3715,1942],{},[613,3717,3718,3720],{},[606,3719,608],{},[606,3721,1949],{},[597,3723,621],{},[613,3725,3726,3728],{},[606,3727,608],{},[606,3729,1958],{},[597,3731,1942],{},[597,3733,1963],{},[597,3735,599],{},[613,3737,3738,3740],{},[606,3739,608],{},[584,3741,3742,3744,3746],{},[606,3743,608],{},[597,3745,1942],{},[613,3747,3748,3750],{},[606,3749,608],{},[606,3751,1939],{},[597,3753,599],{},[613,3755,3756,3758],{},[606,3757,1939],{},[606,3759,3760],{},"3",[639,3762,3763],{"encoding":641},"1 - \\frac{1}{2} + \\frac{1}{4} - \\frac{1}{8} + \\ldots = \\frac{1}{1 + \\frac{1}{2}} = \\frac{2}{3}",[568,3765,3767,3786,3863,3940,4017,4035,4192],{"className":3766,"ariaHidden":647},[646],[568,3768,3770,3774,3777,3780,3783],{"className":3769},[651],[568,3771],{"className":3772,"style":3773},[655],"height:0.7278em;vertical-align:-0.0833em;",[568,3775,608],{"className":3776},[660],[568,3778],{"className":3779,"style":778},[718],[568,3781,621],{"className":3782},[782],[568,3784],{"className":3785,"style":778},[718],[568,3787,3789,3792,3854,3857,3860],{"className":3788},[651],[568,3790],{"className":3791,"style":1995},[655],[568,3793,3795,3798,3851],{"className":3794},[660],[568,3796],{"className":3797},[799,800],[568,3799,3801],{"className":3800},[613],[568,3802,3804,3843],{"className":3803},[672,673],[568,3805,3807,3840],{"className":3806},[677],[568,3808,3810,3821,3829],{"className":3809,"style":2014},[681],[568,3811,3812,3815],{"style":2017},[568,3813],{"className":3814,"style":820},[689],[568,3816,3818],{"className":3817},[660],[568,3819,1939],{"className":3820},[660],[568,3822,3823,3826],{"style":839},[568,3824],{"className":3825,"style":820},[689],[568,3827],{"className":3828,"style":847},[846],[568,3830,3831,3834],{"style":2037},[568,3832],{"className":3833,"style":820},[689],[568,3835,3837],{"className":3836},[660],[568,3838,608],{"className":3839},[660],[568,3841,705],{"className":3842},[704],[568,3844,3846],{"className":3845},[677],[568,3847,3849],{"className":3848,"style":2056},[681],[568,3850],{},[568,3852],{"className":3853},[915,800],[568,3855],{"className":3856,"style":778},[718],[568,3858,1942],{"className":3859},[782],[568,3861],{"className":3862,"style":778},[718],[568,3864,3866,3869,3931,3934,3937],{"className":3865},[651],[568,3867],{"className":3868,"style":1995},[655],[568,3870,3872,3875,3928],{"className":3871},[660],[568,3873],{"className":3874},[799,800],[568,3876,3878],{"className":3877},[613],[568,3879,3881,3920],{"className":3880},[672,673],[568,3882,3884,3917],{"className":3883},[677],[568,3885,3887,3898,3906],{"className":3886,"style":2014},[681],[568,3888,3889,3892],{"style":2017},[568,3890],{"className":3891,"style":820},[689],[568,3893,3895],{"className":3894},[660],[568,3896,1949],{"className":3897},[660],[568,3899,3900,3903],{"style":839},[568,3901],{"className":3902,"style":820},[689],[568,3904],{"className":3905,"style":847},[846],[568,3907,3908,3911],{"style":2037},[568,3909],{"className":3910,"style":820},[689],[568,3912,3914],{"className":3913},[660],[568,3915,608],{"className":3916},[660],[568,3918,705],{"className":3919},[704],[568,3921,3923],{"className":3922},[677],[568,3924,3926],{"className":3925,"style":2056},[681],[568,3927],{},[568,3929],{"className":3930},[915,800],[568,3932],{"className":3933,"style":778},[718],[568,3935,621],{"className":3936},[782],[568,3938],{"className":3939,"style":778},[718],[568,3941,3943,3946,4008,4011,4014],{"className":3942},[651],[568,3944],{"className":3945,"style":1995},[655],[568,3947,3949,3952,4005],{"className":3948},[660],[568,3950],{"className":3951},[799,800],[568,3953,3955],{"className":3954},[613],[568,3956,3958,3997],{"className":3957},[672,673],[568,3959,3961,3994],{"className":3960},[677],[568,3962,3964,3975,3983],{"className":3963,"style":2014},[681],[568,3965,3966,3969],{"style":2017},[568,3967],{"className":3968,"style":820},[689],[568,3970,3972],{"className":3971},[660],[568,3973,1958],{"className":3974},[660],[568,3976,3977,3980],{"style":839},[568,3978],{"className":3979,"style":820},[689],[568,3981],{"className":3982,"style":847},[846],[568,3984,3985,3988],{"style":2037},[568,3986],{"className":3987,"style":820},[689],[568,3989,3991],{"className":3990},[660],[568,3992,608],{"className":3993},[660],[568,3995,705],{"className":3996},[704],[568,3998,4000],{"className":3999},[677],[568,4001,4003],{"className":4002,"style":2056},[681],[568,4004],{},[568,4006],{"className":4007},[915,800],[568,4009],{"className":4010,"style":778},[718],[568,4012,1942],{"className":4013},[782],[568,4015],{"className":4016,"style":778},[718],[568,4018,4020,4023,4026,4029,4032],{"className":4019},[651],[568,4021],{"className":4022,"style":2231},[655],[568,4024,1963],{"className":4025},[2235],[568,4027],{"className":4028,"style":719},[718],[568,4030,599],{"className":4031},[723],[568,4033],{"className":4034,"style":719},[718],[568,4036,4038,4042,4183,4186,4189],{"className":4037},[651],[568,4039],{"className":4040,"style":4041},[655],"height:2.4015em;vertical-align:-1.0801em;",[568,4043,4045,4048,4180],{"className":4044},[660],[568,4046],{"className":4047},[799,800],[568,4049,4051],{"className":4050},[613],[568,4052,4054,4171],{"className":4053},[672,673],[568,4055,4057,4168],{"className":4056},[677],[568,4058,4060,4149,4157],{"className":4059,"style":2014},[681],[568,4061,4063,4066],{"style":4062},"top:-2.2649em;",[568,4064],{"className":4065,"style":820},[689],[568,4067,4069,4072,4075,4078,4081],{"className":4068},[660],[568,4070,608],{"className":4071},[660],[568,4073],{"className":4074,"style":778},[718],[568,4076,1942]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Fehler",[4265,4266,4267,4619,4962],"ul",{},[4268,4269,4270,4271,4331,4332,4383,4384,1046,4523,4618],"li",{},"Die Formel bei ",[568,4272,4274,4295],{"className":4273},[571],[568,4275,4277],{"className":4276},[575],[577,4278,4279],{"xmlns":579},[581,4280,4281,4293],{},[584,4282,4283,4285,4287,4289,4291],{},[590,4284,932],{"mathvariant":931},[590,4286,627],{},[590,4288,932],{"mathvariant":931},[597,4290,1326],{},[606,4292,608],{},[639,4294,1331],{"encoding":641},[568,4296,4298,4322],{"className":4297,"ariaHidden":647},[646],[568,4299,4301,4304,4307,4310,4313,4316,4319],{"className":4300},[651],[568,4302],{"className":4303,"style":954},[655],[568,4305,932],{"className":4306},[660],[568,4308,627],{"className":4309,"style":836},[660,664],[568,4311,932],{"className":4312},[660],[568,4314],{"className":4315,"style":719},[718],[568,4317,1326],{"className":4318},[723],[568,4320],{"className":4321,"style":719},[718],[568,4323,4325,4328],{"className":4324},[651],[568,4326],{"className":4327,"style":979},[655],[568,4329,608],{"className":4330},[660]," anwenden. Für ",[568,4333,4335,4353],{"className":4334},[571],[568,4336,4338],{"className":4337},[575],[577,4339,4340],{"xmlns":579},[581,4341,4342,4350],{},[584,4343,4344,4346,4348],{},[590,4345,627],{},[597,4347,599],{},[606,4349,1939],{},[639,4351,4352],{"encoding":641},"q = 2",[568,4354,4356,4374],{"className":4355,"ariaHidden":647},[646],[568,4357,4359,4362,4365,4368,4371],{"className":4358},[651],[568,4360],{"className":4361,"style":2715},[655],[568,4363,627],{"className":4364,"style":836},[660,664],[568,4366],{"className":4367,"style":719},[718],[568,4369,599],{"className":4370},[723],[568,4372],{"className":4373,"style":719},[718],[568,4375,4377,4380],{"className":4376},[651],[568,4378],{"className":4379,"style":979},[655],[568,4381,1939],{"className":4382},[660]," ergäbe sie ",[568,4385,4387,4417],{"className":4386},[571],[568,4388,4390],{"className":4389},[575],[577,4391,4392],{"xmlns":579},[581,4393,4394,4414],{},[584,4395,4396,4408,4410,4412],{},[613,4397,4398,4400],{},[606,4399,608],{},[584,4401,4402,4404,4406],{},[606,4403,608],{},[597,4405,621],{},[606,4407,1939],{},[597,4409,599],{},[597,4411,621],{},[606,4413,608],{},[639,4415,4416],{"encoding":641},"\\frac{1}{1 - 2} = -1",[568,4418,4420,4511],{"className":4419,"ariaHidden":647},[646],[568,4421,4423,4427,4502,4505,4508],{"className":4422},[651],[568,4424],{"className":4425,"style":4426},[655],"height:1.2484em;vertical-align:-0.4033em;",[568,4428,4430,4433,4499],{"className":4429},[660],[568,4431],{"className":4432},[799,800],[568,4434,4436],{"className":4435},[613],[568,4437,4439,4490],{"className":4438},[672,673],[568,4440,4442,4487],{"className":4441},[677],[568,4443,4445,4465,4473],{"className":4444,"style":3635},[681],[568,4446,4447,4450],{"style":816},[568,4448],{"className":4449,"style":820},[689],[568,4451,4453],{"className":4452},[694,695,696,697],[568,4454,4456,4459,4462],{"className":4455},[660,697],[568,4457,608],{"className":4458},[660,697],[568,4460,621],{"className":4461},[782,697],[568,4463,1939],{"className":4464},[660,697],[568,4466,4467,4470],{"style":839},[568,4468],{"className":4469,"style":820},[689],[568,4471],{"className":4472,"style":847},[846],[568,4474,4475,4478],{"style":3660},[568,4476],{"className":4477,"style":820},[689],[568,4479,4481],{"className":4480},[694,695,696,697],[568,4482,4484],{"className":4483},[660,697],[568,4485,608],{"className":4486},[660,697],[568,4488,705],{"className":4489},[704],[568,4491,4493],{"className":4492},[677],[568,4494,4497],{"className":4495,"style":4496},[681],"height:0.4033em;",[568,4498],{},[568,4500],{"className":4501},[915,800],[568,4503],{"className":4504,"style":719},[718],[568,4506,599],{"className":4507},[723],[568,4509],{"className":4510,"style":719},[718],[568,4512,4514,4517,4520],{"className":4513},[651],[568,4515],{"className":4516,"style":3773},[655],[568,4518,621],{"className":4519},[660],[568,4521,608],{"className":4522},[660],[568,4524,4526,4552],{"className":4525},[571],[568,4527,4529],{"className":4528},[575],[577,4530,4531],{"xmlns":579},[581,4532,4533,4549],{},[584,4534,4535,4537,4539,4541,4543,4545,4547],{},[606,4536,608],{},[597,4538,1942],{},[606,4540,1939],{},[597,4542,1942],{},[606,4544,1949],{},[597,4546,1942],{},[597,4548,1963],{},[639,4550,4551],{"encoding":641},"1 + 2 + 4 + \\ldots",[568,4553,4555,4573,4591,4609],{"className":4554,"ariaHidden":647},[646],[568,4556,4558,4561,4564,4567,4570],{"className":4557},[651],[568,4559],{"className":4560,"style":3773},[655],[568,4562,608],{"className":4563},[660],[568,4565],{"className":4566,"style":778},[718],[568,4568,1942],{"className":4569},[782],[568,4571],{"className":4572,"style":778},[718],[568,4574,4576,4579,4582,4585,4588],{"className":4575},[651],[568,4577],{"className":4578,"style":3773},[655],[568,4580,1939],{"className":4581},[660],[568,4583],{"className":4584,"style":778},[718],[568,4586,1942],{"className":4587},[782],[568,4589],{"className":4590,"style":778},[718],[568,4592,4594,4597,4600,4603,4606],{"className":4593},[651],[568,4595],{"className":4596,"style":3773},[655],[568,4598,1949],{"className":4599},[660],[568,4601],{"className":4602,"style":778},[718],[568,4604,1942],{"className":4605},[782],[568,4607],{"className":4608,"style":778},[718],[568,4610,4612,4615],{"className":4611},[651],[568,4613],{"className":4614,"style":2577},[655],[568,4616,1963],{"className":4617},[2235],", obwohl die Reihe gegen unendlich geht.",[4268,4620,4621,4622,4833,4834,4932,4933,4961],{},"Mit dem falschen ersten Glied rechnen. Im Zähler steht das erste tatsächlich addierte Glied: Bei ",[568,4623,4625,4655],{"className":4624},[571],[568,4626,4628],{"className":4627},[575],[577,4629,4630],{"xmlns":579},[581,4631,4632,4652],{},[584,4633,4634,4640,4642,4648,4650],{},[613,4635,4636,4638],{},[606,4637,608],{},[606,4639,1939],{},[597,4641,1942],{},[613,4643,4644,4646],{},[606,4645,608],{},[606,4647,1949],{},[597,4649,1942],{},[597,4651,1963],{},[639,4653,4654],{"encoding":641},"\\frac{1}{2} + \\frac{1}{4} + \\ldots",[568,4656,4658,4741,4824],{"className":4657,"ariaHidden":647},[646],[568,4659,4661,4664,4732,4735,4738],{"className":4660},[651],[568,4662],{"className":4663,"style":3613},[655],[568,4665,4667,4670,4729],{"className":4666},[660],[568,4668],{"className":4669},[799,800],[568,4671,4673],{"className":4672},[613],[568,4674,4676,4721],{"className":4675},[672,673],[568,4677,4679,4718],{"className":4678},[677],[568,4680,4682,4696,4704],{"className":4681,"style":3635},[681],[568,4683,4684,4687],{"style":816},[568,4685],{"className":4686,"style":820},[689],[568,4688,4690],{"className":4689},[694,695,696,697],[568,4691,4693],{"className":4692},[660,697],[568,4694,1939],{"className":4695},[660,697],[568,4697,4698,4701],{"style":839},[568,4699],{"className":4700,"style":820},[689],[568,4702],{"className":4703,"style":847},[846],[568,4705,4706,4709],{"style":3660},[568,4707],{"className":4708,"style":820},[689],[568,4710,4712],{"className":4711},[694,695,696,697],[568,4713,4715],{"className":4714},[660,697],[568,4716,608],{"className":4717},[660,697],[568,4719,705],{"className":4720},[704],[568,4722,4724],{"className":4723},[677],[568,4725,4727],{"className":4726,"style":3682},[681],[568,4728],{},[568,4730],{"className":4731},[915,800],[568,4733],{"className":4734,"style":778},[718],[568,4736,1942],{"className":4737},[782],[568,4739],{"className":4740,"style":778},[718],[568,4742,4744,4747,4815,4818,4821],{"className":4743},[651],[568,4745],{"className":4746,"style":3613},[655],[568,4748,4750,4753,4812],{"className":4749},[660],[568,4751],{"className":4752},[799,800],[568,4754,4756],{"className":4755},[613],[568,4757,4759,4804],{"className":4758},[672,673],[568,4760,4762,4801],{"className":4761},[677],[568,4763,4765,4779,4787],{"className":4764,"style":3635},[681],[568,4766,4767,4770],{"style":816},[568,4768],{"className":4769,"style":820},[689],[568,4771,4773],{"className":4772},[694,695,696,697],[568,4774,4776],{"className":4775},[660,697],[568,4777,1949],{"className":4778},[660,697],[568,4780,4781,4784],{"style":839},[568,4782],{"className":4783,"style":820},[689],[568,4785],{"className":4786,"style":847},[846],[568,4788,4789,4792],{"style":3660},[568,4790],{"className":4791,"style":820},[689],[568,4793,4795],{"className":4794},[694,695,696,697],[568,4796,4798],{"className":4797},[660,697],[568,4799,608],{"className":4800},[660,697],[568,4802,705],{"className":4803},[704],[568,4805,4807],{"className":4806},[677],[568,4808,4810],{"className":4809,"style":3682},[681],[568,4811],{},[568,4813],{"className":4814},[915,800],[568,4816],{"className":4817,"style":778},[718],[568,4819,1942],{"className":4820},[782],[568,4822],{"className":4823,"style":778},[718],[568,4825,4827,4830],{"className":4826},[651],[568,4828],{"className":4829,"style":2577},[655],[568,4831,1963],{"className":4832},[2235]," ist das ",[568,4835,4837,4855],{"className":4836},[571],[568,4838,4840],{"className":4839},[575],[577,4841,4842],{"xmlns":579},[581,4843,4844,4852],{},[584,4845,4846],{},[613,4847,4848,4850],{},[606,4849,608],{},[606,4851,1939],{},[639,4853,4854],{"encoding":641},"\\frac{1}{2}",[568,4856,4858],{"className":4857,"ariaHidden":647},[646],[568,4859,4861,4864],{"className":4860},[651],[568,4862],{"className":4863,"style":3613},[655],[568,4865,4867,4870,4929],{"className":4866},[660],[568,4868],{"className":4869},[799,800],[568,4871,4873],{"className":4872},[613],[568,4874,4876,4921],{"className":4875},[672,673],[568,4877,4879,4918],{"className":4878},[677],[568,4880,4882,4896,4904],{"className":4881,"style":3635},[681],[568,4883,4884,4887],{"style":816},[568,4885],{"className":4886,"style":820},[689],[568,4888,4890],{"className":4889},[694,695,696,697],[568,4891,4893],{"className":4892},[660,697],[568,4894,1939],{"className":4895},[660,697],[568,4897,4898,4901],{"style":839},[568,4899],{"className":4900,"style":820},[689],[568,4902],{"className":4903,"style":847},[846],[568,4905,4906,4909],{"style":3660},[568,4907],{"className":4908,"style":820},[689],[568,4910,4912],{"className":4911},[694,695,696,697],[568,4913,4915],{"className":4914},[660,697],[568,4916,608],{"className":4917},[660,697],[568,4919,705],{"className":4920},[704],[568,4922,4924],{"className":4923},[677],[568,4925,4927],{"className":4926,"style":3682},[681],[568,4928],{},[568,4930],{"className":4931},[915,800],", nicht ",[568,4934,4936,4949],{"className":4935},[571],[568,4937,4939],{"className":4938},[575],[577,4940,4941],{"xmlns":579},[581,4942,4943,4947],{},[584,4944,4945],{},[606,4946,608],{},[639,4948,608],{"encoding":641},[568,4950,4952],{"className":4951,"ariaHidden":647},[646],[568,4953,4955,4958],{"className":4954},[651],[568,4956],{"className":4957,"style":979},[655],[568,4959,608],{"className":4960},[660],".",[4268,4963,4964,4965,4993,4994,4961],{},"Bei negativem ",[568,4966,4968,4981],{"className":4967},[571],[568,4969,4971],{"className":4970},[575],[577,4972,4973],{"xmlns":579},[581,4974,4975,4979],{},[584,4976,4977],{},[590,4978,627],{},[639,4980,627],{"encoding":641},[568,4982,4984],{"className":4983,"ariaHidden":647},[646],[568,4985,4987,4990],{"className":4986},[651],[568,4988],{"className":4989,"style":2715},[655],[568,4991,627],{"className":4992,"style":836},[660,664]," das Vorzeichen im Nenner falsch auflösen: ",[568,4995,4997,5036],{"className":4996},[571],[568,4998,5000],{"className":4999},[575],[577,5001,5002],{"xmlns":579},[581,5003,5004,5033],{},[584,5005,5006,5008,5010,5014,5016,5022,5025,5027],{},[606,5007,608],{},[597,5009,621],{},[597,5011,5013],{"stretchy":5012},"false","(",[597,5015,621],{},[613,5017,5018,5020],{},[606,5019,608],{},[606,5021,1939],{},[597,5023,5024],{"stretchy":5012},")",[597,5026,599],{},[613,5028,5029,5031],{},[606,5030,3760],{},[606,5032,1939],{},[639,5034,5035],{"encoding":641},"1 - (-\\frac{1}{2}) = \\frac{3}{2}",[568,5037,5039,5057,5149],{"className":5038,"ariaHidden":647},[646],[568,5040,5042,5045,5048,5051,5054],{"className":5041},[651],[568,5043],{"className":5044,"style":3773},[655],[568,5046,608],{"className":5047},[660],[568,5049],{"className":5050,"style":778},[718],[568,5052,621],{"className":5053},[782],[568,5055],{"className":5056,"style":778},[718],[568,5058,5060,5063,5066,5069,5137,5140,5143,5146],{"className":5059},[651],[568,5061],{"className":5062,"style":3613},[655],[568,5064,5013],{"className":5065},[799],[568,5067,621],{"className":5068},[660],[568,5070,5072,5075,5134],{"className":5071},[660],[568,5073],{"className":5074},[799,800],[568,5076,5078],{"className":5077},[613],[568,5079,5081,5126],{"className":5080},[672,673],[568,5082,5084,5123],{"className":5083},[677],[568,5085,5087,5101,5109],{"className":5086,"style":3635},[681],[568,5088,5089,5092],{"style":816},[568,5090],{"className":5091,"style":820},[689],[568,5093,5095],{"className":5094},[694,695,696,697],[568,5096,5098],{"className":5097},[660,697],[568,5099,1939],{"className":5100},[660,697],[568,5102,5103,5106],{"style":839},[568,5104],{"className":5105,"style":820},[689],[568,5107],{"className":5108,"style":847},[846],[568,5110,5111,5114],{"style":3660},[568,5112],{"className":5113,"style":820},[689],[568,5115,5117],{"className":5116},[694,695,696,697],[568,5118,5120],{"className":5119},[660,697],[568,5121,608],{"className":5122},[660,697],[568,5124,705],{"className":5125},[704],[568,5127,5129],{"className":5128},[677],[568,5130,5132],{"className":5131,"style":3682},[681],[568,5133],{},[568,5135],{"className":5136},[915,800],[568,5138,5024],{"className":5139},[915],[568,5141],{"className":5142,"style":719},[718],[568,5144,599],{"className":5145},[723],[568,5147],{"className":5148,"style":719},[718],[568,5150,5152,5155],{"className":5151},[651],[568,5153],{"className":5154,"style":3613},[655],[568,5156,5158,5161,5220],{"className":5157},[660],[568,5159],{"className":5160},[799,800],[568,5162,5164],{"className":5163},[613],[568,5165,5167,5212],{"className":5166},[672,673],[568,5168,5170,5209],{"className":5169},[677],[568,5171,5173,5187,5195],{"className":5172,"style":3635},[681],[568,5174,5175,5178],{"style":816},[568,5176],{"className":5177,"style":820},[689],[568,5179,5181],{"className":5180},[694,695,696,697],[568,5182,5184],{"className":5183},[660,697],[568,5185,1939],{"className":5186},[660,697],[568,5188,5189,5192],{"style":839},[568,5190],{"className":5191,"style":820},[689],[568,5193],{"className":5194,"style":847},[846],[568,5196,5197,5200],{"style":3660},[568,5198],{"className":5199,"style":820},[689],[568,5201,5203],{"className":5202},[694,695,696,697],[568,5204,5206],{"className":5205},[660,697],[568,5207,3760],{"className":5208},[660,697],[568,5210,705],{"className":5211},[704],[568,5213,5215],{"className":5214},[677],[568,5216,5218],{"className":5217,"style":3682},[681],[568,5219],{},[568,5221],{"className":5222},[915,800],{"title":5224,"searchDepth":5225,"depth":5225,"links":5226},"",2,[5227,5228,5229],{"id":561,"depth":5225,"text":562},{"id":1911,"depth":5225,"text":1912},{"id":4262,"depth":5225,"text":4263},[5231,5234,5236,5238,5240,5243,5245,5248,5251],{"lhs":5232,"rhs":5233},"a1\u002F(1 - q) - a1*(1 - q^n)\u002F(1 - q)","a1*q^n\u002F(1 - q)",{"lhs":5235,"rhs":608},"0.5\u002F(1 - 0.5)",{"lhs":5237,"rhs":608},"round(sum(0.5.^(1:60)), 12)",{"lhs":5239,"rhs":608},"0.9\u002F(1 - 0.1)",{"lhs":5241,"rhs":5242},"0.36\u002F(1 - 0.01)","36\u002F99",{"lhs":5242,"rhs":5244},"4\u002F11",{"lhs":5246,"rhs":5247},"round(sum(0.36*0.01.^(0:20)), 12)","round(4\u002F11, 12)",{"lhs":5249,"rhs":5250},"1\u002F(1 - (-0.5))","2\u002F3",{"lhs":5252,"rhs":5253},"round(sum((-0.5).^(0:60)), 12)","round(2\u002F3, 12)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmi>q\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmo><\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">|q| < 1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\"><\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","geometric-series","\\sum_{k=0}^{\\infty} a_1 q^k = a_1 + a_1 q + a_1 q^2 + \\ldots = \\frac{a_1}{1 - q}","\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>\u003Cmunderover>\u003Cmo>∑\u003C\u002Fmo>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cmi 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