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",[573,1171,1173,1196],{"className":1172},[580],[573,1174,1176],{"className":1175},[584],[586,1177,1178],{"xmlns":588},[591,1179,1180,1193],{},[594,1181,1182,1188,1190],{},[600,1183,1184,1186],{},[603,1185,605],{},[616,1187,618],{},[612,1189,1132],{},[616,1191,1192],{},"0",[657,1194,1195],{"encoding":659},"a_1 > 0",[573,1197,1199,1255],{"className":1198,"ariaHidden":644},[664],[573,1200,1202,1206,1246,1249,1252],{"className":1201},[668],[573,1203],{"className":1204,"style":1205},[672],"height:0.6891em;vertical-align:-0.15em;",[573,1207,1209,1212],{"className":1208},[677],[573,1210,605],{"className":1211},[677,717],[573,1213,1215],{"className":1214},[721],[573,1216,1218,1238],{"className":1217},[689,690],[573,1219,1221,1235],{"className":1220},[694],[573,1222,1224],{"className":1223,"style":801},[698],[573,1225,1226,1229],{"style":734},[573,1227],{"className":1228,"style":738},[706],[573,1230,1232],{"className":1231},[742,743,744,745],[573,1233,618],{"className":1234},[677,745],[573,1236,753],{"className":1237},[752],[573,1239,1241],{"className":1240},[694],[573,1242,1244],{"className":1243,"style":760},[698],[573,1245],{},[573,1247],{"className":1248,"style":854},[632],[573,1250,1132],{"className":1251},[858],[573,1253],{"className":1254,"style":854},[632],[573,1256,1258,1261],{"className":1257},[668],[573,1259],{"className":1260,"style":1044},[672],[573,1262,1192],{"className":1263},[677]," exponentielles Wachstum).",[1114,1266,1267,1342,1343,1371],{},[573,1268,1270,1293],{"className":1269},[580],[573,1271,1273],{"className":1272},[584],[586,1274,1275],{"xmlns":588},[591,1276,1277,1290],{},[594,1278,1279,1281,1284,1286,1288],{},[616,1280,1192],{},[612,1282,1283],{},"\u003C",[603,1285,630],{},[612,1287,1283],{},[616,1289,618],{},[657,1291,1292],{"encoding":659},"0 \u003C q \u003C 1",[573,1294,1296,1315,1333],{"className":1295,"ariaHidden":644},[664],[573,1297,1299,1303,1306,1309,1312],{"className":1298},[668],[573,1300],{"className":1301,"style":1302},[672],"height:0.6835em;vertical-align:-0.0391em;",[573,1304,1192],{"className":1305},[677],[573,1307],{"className":1308,"style":854},[632],[573,1310,1283],{"className":1311},[858],[573,1313],{"className":1314,"style":854},[632],[573,1316,1318,1321,1324,1327,1330],{"className":1317},[668],[573,1319],{"className":1320,"style":1147},[672],[573,1322,630],{"className":1323,"style":872},[677,717],[573,1325],{"className":1326,"style":854},[632],[573,1328,1283],{"className":1329},[858],[573,1331],{"className":1332,"style":854},[632],[573,1334,1336,1339],{"className":1335},[668],[573,1337],{"className":1338,"style":1044},[672],[573,1340,618],{"className":1341},[677],": Die Glieder nähern sich ",[573,1344,1346,1359],{"className":1345},[580],[573,1347,1349],{"className":1348},[584],[586,1350,1351],{"xmlns":588},[591,1352,1353,1357],{},[594,1354,1355],{},[616,1356,1192],{},[657,1358,1192],{"encoding":659},[573,1360,1362],{"className":1361,"ariaHidden":644},[664],[573,1363,1365,1368],{"className":1364},[668],[573,1366],{"className":1367,"style":1044},[672],[573,1369,1192],{"className":1370},[677]," (exponentielle Abnahme).",[1114,1373,1374,1425,1426,1429],{},[573,1375,1377,1395],{"className":1376},[580],[573,1378,1380],{"className":1379},[584],[586,1381,1382],{"xmlns":588},[591,1383,1384,1392],{},[594,1385,1386,1388,1390],{},[603,1387,630],{},[612,1389,1283],{},[616,1391,1192],{},[657,1393,1394],{"encoding":659},"q \u003C 0",[573,1396,1398,1416],{"className":1397,"ariaHidden":644},[664],[573,1399,1401,1404,1407,1410,1413],{"className":1400},[668],[573,1402],{"className":1403,"style":1147},[672],[573,1405,630],{"className":1406,"style":872},[677,717],[573,1408],{"className":1409,"style":854},[632],[573,1411,1283],{"className":1412},[858],[573,1414],{"className":1415,"style":854},[632],[573,1417,1419,1422],{"className":1418},[668],[573,1420],{"className":1421,"style":1044},[672],[573,1423,1192],{"className":1424},[677],": Die Vorzeichen wechseln ab, man spricht von einer ",[568,1427,1428],{},"alternierenden"," Folge.",[564,1431,1432,1433,1704,1705,1797,1798,1849],{},"Geometrische Folgen sind das diskrete Gegenstück zu Exponentialfunktionen: ",[573,1434,1436,1476],{"className":1435},[580],[573,1437,1439],{"className":1438},[584],[586,1440,1441],{"xmlns":588},[591,1442,1443,1473],{},[594,1444,1445,1451,1453,1463,1466],{},[600,1446,1447,1449],{},[603,1448,605],{},[603,1450,610],{},[612,1452,627],{},[597,1454,1455,1461],{},[600,1456,1457,1459],{},[603,1458,605],{},[616,1460,618],{},[603,1462,630],{},[612,1464,1465],{},"⋅",[1467,1468,1469,1471],"msup",{},[603,1470,630],{},[603,1472,610],{},[657,1474,1475],{"encoding":659},"a_n = \\frac{a_1}{q} \\cdot q^n",[573,1477,1479,1535,1666],{"className":1478,"ariaHidden":644},[664],[573,1480,1482,1486,1526,1529,1532],{"className":1481},[668],[573,1483],{"className":1484,"style":1485},[672],"height:0.5806em;vertical-align:-0.15em;",[573,1487,1489,1492],{"className":1488},[677],[573,1490,605],{"className":1491},[677,717],[573,1493,1495],{"className":1494},[721],[573,1496,1498,1518],{"className":1497},[689,690],[573,1499,1501,1515],{"className":1500},[694],[573,1502,1504],{"className":1503,"style":731},[698],[573,1505,1506,1509],{"style":734},[573,1507],{"className":1508,"style":738},[706],[573,1510,1512],{"className":1511},[742,743,744,745],[573,1513,610],{"className":1514},[677,717,745],[573,1516,753],{"className":1517},[752],[573,1519,1521],{"className":1520},[694],[573,1522,1524],{"className":1523,"style":760},[698],[573,1525],{},[573,1527],{"className":1528,"style":854},[632],[573,1530,627],{"className":1531},[858],[573,1533],{"className":1534,"style":854},[632],[573,1536,1538,1542,1657,1660,1663],{"className":1537},[668],[573,1539],{"className":1540,"style":1541},[672],"height:1.1926em;vertical-align:-0.4811em;",[573,1543,1545,1548,1654],{"className":1544},[677],[573,1546],{"className":1547},[681,682],[573,1549,1551],{"className":1550},[597],[573,1552,1554,1645],{"className":1553},[689,690],[573,1555,1557,1642],{"className":1556},[694],[573,1558,1561,1576,1584],{"className":1559,"style":1560},[698],"height:0.7115em;",[573,1562,1564,1567],{"style":1563},"top:-2.655em;",[573,1565],{"className":1566,"style":707},[706],[573,1568,1570],{"className":1569},[742,743,744,745],[573,1571,1573],{"className":1572},[677,745],[573,1574,630],{"className":1575,"style":872},[677,717,745],[573,1577,1578,1581],{"style":765},[573,1579],{"className":1580,"style":707},[706],[573,1582],{"className":1583,"style":773},[772],[573,1585,1587,1590],{"style":1586},"top:-3.4101em;",[573,1588],{"className":1589,"style":707},[706],[573,1591,1593],{"className":1592},[742,743,744,745],[573,1594,1596],{"className":1595},[677,745],[573,1597,1599,1602],{"className":1598},[677,745],[573,1600,605],{"className":1601},[677,717,745],[573,1603,1605],{"className":1604},[721],[573,1606,1608,1633],{"className":1607},[689,690],[573,1609,1611,1630],{"className":1610},[694],[573,1612,1615],{"className":1613,"style":1614},[698],"height:0.3173em;",[573,1616,1618,1622],{"style":1617},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[573,1619],{"className":1620,"style":1621},[706],"height:2.5em;",[573,1623,1627],{"className":1624},[742,1625,1626,745],"reset-size3","size1",[573,1628,618],{"className":1629},[677,745],[573,1631,753],{"className":1632},[752],[573,1634,1636],{"className":1635},[694],[573,1637,1640],{"className":1638,"style":1639},[698],"height:0.143em;",[573,1641],{},[573,1643,753],{"className":1644},[752],[573,1646,1648],{"className":1647},[694],[573,1649,1652],{"className":1650,"style":1651},[698],"height:0.4811em;",[573,1653],{},[573,1655],{"className":1656},[850,682],[573,1658],{"className":1659,"style":1031},[632],[573,1661,1465],{"className":1662},[819],[573,1664],{"className":1665,"style":1031},[632],[573,1667,1669,1673],{"className":1668},[668],[573,1670],{"className":1671,"style":1672},[672],"height:0.8588em;vertical-align:-0.1944em;",[573,1674,1676,1679],{"className":1675},[677],[573,1677,630],{"className":1678,"style":872},[677,717],[573,1680,1682],{"className":1681},[721],[573,1683,1685],{"className":1684},[689],[573,1686,1688],{"className":1687},[694],[573,1689,1692],{"className":1690,"style":1691},[698],"height:0.6644em;",[573,1693,1695,1698],{"style":1694},"top:-3.063em;margin-right:0.05em;",[573,1696],{"className":1697,"style":738},[706],[573,1699,1701],{"className":1700},[742,743,744,745],[573,1702,610],{"className":1703},[677,717,745],". Typische Anwendungen sind Wachstums- und Zerfallsprozesse in festen Zeitschritten. ",[573,1706,1708,1730],{"className":1707},[580],[573,1709,1711],{"className":1710},[584],[586,1712,1713],{"xmlns":588},[591,1714,1715,1727],{},[594,1716,1717,1723,1725],{},[600,1718,1719,1721],{},[603,1720,605],{},[616,1722,618],{},[612,1724,627],{},[616,1726,1192],{},[657,1728,1729],{"encoding":659},"a_1 = 0",[573,1731,1733,1788],{"className":1732,"ariaHidden":644},[664],[573,1734,1736,1739,1779,1782,1785],{"className":1735},[668],[573,1737],{"className":1738,"style":1485},[672],[573,1740,1742,1745],{"className":1741},[677],[573,1743,605],{"className":1744},[677,717],[573,1746,1748],{"className":1747},[721],[573,1749,1751,1771],{"className":1750},[689,690],[573,1752,1754,1768],{"className":1753},[694],[573,1755,1757],{"className":1756,"style":801},[698],[573,1758,1759,1762],{"style":734},[573,1760],{"className":1761,"style":738},[706],[573,1763,1765],{"className":1764},[742,743,744,745],[573,1766,618],{"className":1767},[677,745],[573,1769,753],{"className":1770},[752],[573,1772,1774],{"className":1773},[694],[573,1775,1777],{"className":1776,"style":760},[698],[573,1778],{},[573,1780],{"className":1781,"style":854},[632],[573,1783,627],{"className":1784},[858],[573,1786],{"className":1787,"style":854},[632],[573,1789,1791,1794],{"className":1790},[668],[573,1792],{"className":1793,"style":1044},[672],[573,1795,1192],{"className":1796},[677]," und ",[573,1799,1801,1819],{"className":1800},[580],[573,1802,1804],{"className":1803},[584],[586,1805,1806],{"xmlns":588},[591,1807,1808,1816],{},[594,1809,1810,1812,1814],{},[603,1811,630],{},[612,1813,627],{},[616,1815,1192],{},[657,1817,1818],{"encoding":659},"q = 0",[573,1820,1822,1840],{"className":1821,"ariaHidden":644},[664],[573,1823,1825,1828,1831,1834,1837],{"className":1824},[668],[573,1826],{"className":1827,"style":954},[672],[573,1829,630],{"className":1830,"style":872},[677,717],[573,1832],{"className":1833,"style":854},[632],[573,1835,627],{"className":1836},[858],[573,1838],{"className":1839,"style":854},[632],[573,1841,1843,1846],{"className":1842},[668],[573,1844],{"className":1845,"style":1044},[672],[573,1847,1192],{"className":1848},[677]," werden ausgeschlossen, weil sonst der Quotient nicht gebildet werden kann.",[559,1851,1853],{"id":1852},"beispiele","Beispiele",[564,1855,1856,1857,1948,1949,1797,2041,2093],{},"Die Folge ",[573,1858,1860,1896],{"className":1859},[580],[573,1861,1863],{"className":1862},[584],[586,1864,1865],{"xmlns":588},[591,1866,1867,1893],{},[594,1868,1869,1872,1875,1878,1880,1883,1885,1888,1890],{},[616,1870,1871],{},"3",[612,1873,1874],{"separator":644},",",[616,1876,1877],{},"6",[612,1879,1874],{"separator":644},[616,1881,1882],{},"12",[612,1884,1874],{"separator":644},[616,1886,1887],{},"24",[612,1889,1874],{"separator":644},[612,1891,1892],{},"…",[657,1894,1895],{"encoding":659},"3, 6, 12, 24, \\ldots",[573,1897,1899],{"className":1898,"ariaHidden":644},[664],[573,1900,1902,1906,1909,1913,1917,1920,1923,1926,1929,1932,1935,1938,1941,1944],{"className":1901},[668],[573,1903],{"className":1904,"style":1905},[672],"height:0.8389em;vertical-align:-0.1944em;",[573,1907,1871],{"className":1908},[677],[573,1910,1874],{"className":1911},[1912],"mpunct",[573,1914],{"className":1915,"style":1916},[632],"margin-right:0.1667em;",[573,1918,1877],{"className":1919},[677],[573,1921,1874],{"className":1922},[1912],[573,1924],{"className":1925,"style":1916},[632],[573,1927,1882],{"className":1928},[677],[573,1930,1874],{"className":1931},[1912],[573,1933],{"className":1934,"style":1916},[632],[573,1936,1887],{"className":1937},[677],[573,1939,1874],{"className":1940},[1912],[573,1942],{"className":1943,"style":1916},[632],[573,1945,1892],{"className":1946},[1947],"minner"," hat ",[573,1950,1952,1974],{"className":1951},[580],[573,1953,1955],{"className":1954},[584],[586,1956,1957],{"xmlns":588},[591,1958,1959,1971],{},[594,1960,1961,1967,1969],{},[600,1962,1963,1965],{},[603,1964,605],{},[616,1966,618],{},[612,1968,627],{},[616,1970,1871],{},[657,1972,1973],{"encoding":659},"a_1 = 3",[573,1975,1977,2032],{"className":1976,"ariaHidden":644},[664],[573,1978,1980,1983,2023,2026,2029],{"className":1979},[668],[573,1981],{"className":1982,"style":1485},[672],[573,1984,1986,1989],{"className":1985},[677],[573,1987,605],{"className":1988},[677,717],[573,1990,1992],{"className":1991},[721],[573,1993,1995,2015],{"className":1994},[689,690],[573,1996,1998,2012],{"className":1997},[694],[573,1999,2001],{"className":2000,"style":801},[698],[573,2002,2003,2006],{"style":734},[573,2004],{"className":2005,"style":738},[706],[573,2007,2009],{"className":2008},[742,743,744,745],[573,2010,618],{"className":2011},[677,745],[573,2013,753],{"className":2014},[752],[573,2016,2018],{"className":2017},[694],[573,2019,2021],{"className":2020,"style":760},[698],[573,2022],{},[573,2024],{"className":2025,"style":854},[632],[573,2027,627],{"className":2028},[858],[573,2030],{"className":2031,"style":854},[632],[573,2033,2035,2038],{"className":2034},[668],[573,2036],{"className":2037,"style":1044},[672],[573,2039,1871],{"className":2040},[677],[573,2042,2044,2063],{"className":2043},[580],[573,2045,2047],{"className":2046},[584],[586,2048,2049],{"xmlns":588},[591,2050,2051,2060],{},[594,2052,2053,2055,2057],{},[603,2054,630],{},[612,2056,627],{},[616,2058,2059],{},"2",[657,2061,2062],{"encoding":659},"q = 2",[573,2064,2066,2084],{"className":2065,"ariaHidden":644},[664],[573,2067,2069,2072,2075,2078,2081],{"className":2068},[668],[573,2070],{"className":2071,"style":954},[672],[573,2073,630],{"className":2074,"style":872},[677,717],[573,2076],{"className":2077,"style":854},[632],[573,2079,627],{"className":2080},[858],[573,2082],{"className":2083,"style":854},[632],[573,2085,2087,2090],{"className":2086},[668],[573,2088],{"className":2089,"style":1044},[672],[573,2091,2059],{"className":2092},[677],". Das achte Glied ist",[573,2095,2097],{"className":2096},[576],[573,2098,2100,2146],{"className":2099},[580],[573,2101,2103],{"className":2102},[584],[586,2104,2105],{"xmlns":588,"display":589},[591,2106,2107,2143],{},[594,2108,2109,2116,2118,2120,2122,2129,2131,2133,2135,2138,2140],{},[600,2110,2111,2113],{},[603,2112,605],{},[616,2114,2115],{},"8",[612,2117,627],{},[616,2119,1871],{},[612,2121,1465],{},[1467,2123,2124,2126],{},[616,2125,2059],{},[616,2127,2128],{},"7",[612,2130,627],{},[616,2132,1871],{},[612,2134,1465],{},[616,2136,2137],{},"128",[612,2139,627],{},[616,2141,2142],{},"384",[657,2144,2145],{"encoding":659},"a_8 = 3 \\cdot 2^7 = 3 \\cdot 128 = 384",[573,2147,2149,2204,2222,2268,2286,2304],{"className":2148,"ariaHidden":644},[664],[573,2150,2152,2155,2195,2198,2201],{"className":2151},[668],[573,2153],{"className":2154,"style":1485},[672],[573,2156,2158,2161],{"className":2157},[677],[573,2159,605],{"className":2160},[677,717],[573,2162,2164],{"className":2163},[721],[573,2165,2167,2187],{"className":2166},[689,690],[573,2168,2170,2184],{"className":2169},[694],[573,2171,2173],{"className":2172,"style":801},[698],[573,2174,2175,2178],{"style":734},[573,2176],{"className":2177,"style":738},[706],[573,2179,2181],{"className":2180},[742,743,744,745],[573,2182,2115],{"className":2183},[677,745],[573,2185,753],{"className":2186},[752],[573,2188,2190],{"className":2189},[694],[573,2191,2193],{"className":2192,"style":760},[698],[573,2194],{},[573,2196],{"className":2197,"style":854},[632],[573,2199,627],{"className":2200},[858],[573,2202],{"className":2203,"style":854},[632],[573,2205,2207,2210,2213,2216,2219],{"className":2206},[668],[573,2208],{"className":2209,"style":1044},[672],[573,2211,1871],{"className":2212},[677],[573,2214],{"className":2215,"style":1031},[632],[573,2217,1465],{"className":2218},[819],[573,2220],{"className":2221,"style":1031},[632],[573,2223,2225,2229,2259,2262,2265],{"className":2224},[668],[573,2226],{"className":2227,"style":2228},[672],"height:0.8641em;",[573,2230,2232,2235],{"className":2231},[677],[573,2233,2059],{"className":2234},[677],[573,2236,2238],{"className":2237},[721],[573,2239,2241],{"className":2240},[689],[573,2242,2244],{"className":2243},[694],[573,2245,2247],{"className":2246,"style":2228},[698],[573,2248,2250,2253],{"style":2249},"top:-3.113em;margin-right:0.05em;",[573,2251],{"className":2252,"style":738},[706],[573,2254,2256],{"className":2255},[742,743,744,745],[573,2257,2128],{"className":2258},[677,745],[573,2260],{"className":2261,"style":854},[632],[573,2263,627],{"className":2264},[858],[573,2266],{"className":2267,"style":854},[632],[573,2269,2271,2274,2277,2280,2283],{"className":2270},[668],[573,2272],{"className":2273,"style":1044},[672],[573,2275,1871],{"className":2276},[677],[573,2278],{"className":2279,"style":1031},[632],[573,2281,1465],{"className":2282},[819],[573,2284],{"className":2285,"style":1031},[632],[573,2287,2289,2292,2295,2298,2301],{"className":2288},[668],[573,2290],{"className":2291,"style":1044},[672],[573,2293,2137],{"className":2294},[677],[573,2296],{"className":2297,"style":854},[632],[573,2299,627],{"className":2300},[858],[573,2302],{"className":2303,"style":854},[632],[573,2305,2307,2310],{"className":2306},[668],[573,2308],{"className":2309,"style":1044},[672],[573,2311,2142],{"className":2312},[677],[564,2314,2315,2316,2361],{},"Ein Ball springt jedes Mal auf die Hälfte der vorigen Höhe. Der erste Sprung ist ",[573,2317,2319,2340],{"className":2318},[580],[573,2320,2322],{"className":2321},[584],[586,2323,2324],{"xmlns":588},[591,2325,2326,2337],{},[594,2327,2328,2331,2334],{},[616,2329,2330],{},"800",[638,2332,2333],{}," ",[638,2335,2336],{},"mm",[657,2338,2339],{"encoding":659},"800\\,\\text{mm}",[573,2341,2343],{"className":2342,"ariaHidden":644},[664],[573,2344,2346,2349,2352,2355],{"className":2345},[668],[573,2347],{"className":2348,"style":1044},[672],[573,2350,2330],{"className":2351},[677],[573,2353],{"className":2354,"style":1916},[632],[573,2356,2358],{"className":2357},[677,880],[573,2359,2336],{"className":2360},[677]," hoch. Der sechste Sprung:",[573,2363,2365],{"className":2364},[576],[573,2366,2368,2409],{"className":2367},[580],[573,2369,2371],{"className":2370},[584],[586,2372,2373],{"xmlns":588,"display":589},[591,2374,2375,2406],{},[594,2376,2377,2383,2385,2387,2389,2397,2399,2402,2404],{},[600,2378,2379,2381],{},[603,2380,605],{},[616,2382,1877],{},[612,2384,627],{},[616,2386,2330],{},[612,2388,1465],{},[1467,2390,2391,2394],{},[616,2392,2393],{},"0,5",[616,2395,2396],{},"5",[612,2398,627],{},[616,2400,2401],{},"25",[638,2403,2333],{},[638,2405,2336],{},[657,2407,2408],{"encoding":659},"a_6 = 800 \\cdot 0{,}5^5 = 25\\,\\text{mm}",[573,2410,2412,2467,2485,2539],{"className":2411,"ariaHidden":644},[664],[573,2413,2415,2418,2458,2461,2464],{"className":2414},[668],[573,2416],{"className":2417,"style":1485},[672],[573,2419,2421,2424],{"className":2420},[677],[573,2422,605],{"className":2423},[677,717],[573,2425,2427],{"className":2426},[721],[573,2428,2430,2450],{"className":2429},[689,690],[573,2431,2433,2447],{"className":2432},[694],[573,2434,2436],{"className":2435,"style":801},[698],[573,2437,2438,2441],{"style":734},[573,2439],{"className":2440,"style":738},[706],[573,2442,2444],{"className":2443},[742,743,744,745],[573,2445,1877],{"className":2446},[677,745],[573,2448,753],{"className":2449},[752],[573,2451,2453],{"className":2452},[694],[573,2454,2456],{"className":2455,"style":760},[698],[573,2457],{},[573,2459],{"className":2460,"style":854},[632],[573,2462,627],{"className":2463},[858],[573,2465],{"className":2466,"style":854},[632],[573,2468,2470,2473,2476,2479,2482],{"className":2469},[668],[573,2471],{"className":2472,"style":1044},[672],[573,2474,2330],{"className":2475},[677],[573,2477],{"className":2478,"style":1031},[632],[573,2480,1465],{"className":2481},[819],[573,2483],{"className":2484,"style":1031},[632],[573,2486,2488,2492,2495,2501,2530,2533,2536],{"className":2487},[668],[573,2489],{"className":2490,"style":2491},[672],"height:1.0585em;vertical-align:-0.1944em;",[573,2493,1192],{"className":2494},[677],[573,2496,2498],{"className":2497},[677],[573,2499,1874],{"className":2500},[1912],[573,2502,2504,2507],{"className":2503},[677],[573,2505,2396],{"className":2506},[677],[573,2508,2510],{"className":2509},[721],[573,2511,2513],{"className":2512},[689],[573,2514,2516],{"className":2515},[694],[573,2517,2519],{"className":2518,"style":2228},[698],[573,2520,2521,2524],{"style":2249},[573,2522],{"className":2523,"style":738},[706],[573,2525,2527],{"className":2526},[742,743,744,745],[573,2528,2396],{"className":2529},[677,745],[573,2531],{"className":2532,"style":854},[632],[573,2534,627],{"className":2535},[858],[573,2537],{"className":2538,"style":854},[632],[573,2540,2542,2545,2548,2551],{"className":2541},[668],[573,2543],{"className":2544,"style":1044},[672],[573,2546,2401],{"className":2547},[677],[573,2549],{"className":2550,"style":1916},[632],[573,2552,2554],{"className":2553},[677,880],[573,2555,2336],{"className":2556},[677],[564,2558,2559,2560,1797,2652,2745,2746,2774],{},"Von einer geometrischen Folge kennt man ",[573,2561,2563,2585],{"className":2562},[580],[573,2564,2566],{"className":2565},[584],[586,2567,2568],{"xmlns":588},[591,2569,2570,2582],{},[594,2571,2572,2578,2580],{},[600,2573,2574,2576],{},[603,2575,605],{},[616,2577,1871],{},[612,2579,627],{},[616,2581,1882],{},[657,2583,2584],{"encoding":659},"a_3 = 12",[573,2586,2588,2643],{"className":2587,"ariaHidden":644},[664],[573,2589,2591,2594,2634,2637,2640],{"className":2590},[668],[573,2592],{"className":2593,"style":1485},[672],[573,2595,2597,2600],{"className":2596},[677],[573,2598,605],{"className":2599},[677,717],[573,2601,2603],{"className":2602},[721],[573,2604,2606,2626],{"className":2605},[689,690],[573,2607,2609,2623],{"className":2608},[694],[573,2610,2612],{"className":2611,"style":801},[698],[573,2613,2614,2617],{"style":734},[573,2615],{"className":2616,"style":738},[706],[573,2618,2620],{"className":2619},[742,743,744,745],[573,2621,1871],{"className":2622},[677,745],[573,2624,753],{"className":2625},[752],[573,2627,2629],{"className":2628},[694],[573,2630,2632],{"className":2631,"style":760},[698],[573,2633],{},[573,2635],{"className":2636,"style":854},[632],[573,2638,627],{"className":2639},[858],[573,2641],{"className":2642,"style":854},[632],[573,2644,2646,2649],{"className":2645},[668],[573,2647],{"className":2648,"style":1044},[672],[573,2650,1882],{"className":2651},[677],[573,2653,2655,2678],{"className":2654},[580],[573,2656,2658],{"className":2657},[584],[586,2659,2660],{"xmlns":588},[591,2661,2662,2675],{},[594,2663,2664,2670,2672],{},[600,2665,2666,2668],{},[603,2667,605],{},[616,2669,1877],{},[612,2671,627],{},[616,2673,2674],{},"96",[657,2676,2677],{"encoding":659},"a_6 = 96",[573,2679,2681,2736],{"className":2680,"ariaHidden":644},[664],[573,2682,2684,2687,2727,2730,2733],{"className":2683},[668],[573,2685],{"className":2686,"style":1485},[672],[573,2688,2690,2693],{"className":2689},[677],[573,2691,605],{"className":2692},[677,717],[573,2694,2696],{"className":2695},[721],[573,2697,2699,2719],{"className":2698},[689,690],[573,2700,2702,2716],{"className":2701},[694],[573,2703,2705],{"className":2704,"style":801},[698],[573,2706,2707,2710],{"style":734},[573,2708],{"className":2709,"style":738},[706],[573,2711,2713],{"className":2712},[742,743,744,745],[573,2714,1877],{"className":2715},[677,745],[573,2717,753],{"className":2718},[752],[573,2720,2722],{"className":2721},[694],[573,2723,2725],{"className":2724,"style":760},[698],[573,2726],{},[573,2728],{"className":2729,"style":854},[632],[573,2731,627],{"className":2732},[858],[573,2734],{"className":2735,"style":854},[632],[573,2737,2739,2742],{"className":2738},[668],[573,2740],{"className":2741,"style":1044},[672],[573,2743,2674],{"className":2744},[677],". Zwischen den Gliedern liegen drei Multiplikationen mit ",[573,2747,2749,2762],{"className":2748},[580],[573,2750,2752],{"className":2751},[584],[586,2753,2754],{"xmlns":588},[591,2755,2756,2760],{},[594,2757,2758],{},[603,2759,630],{},[657,2761,630],{"encoding":659},[573,2763,2765],{"className":2764,"ariaHidden":644},[664],[573,2766,2768,2771],{"className":2767},[668],[573,2769],{"className":2770,"style":954},[672],[573,2772,630],{"className":2773,"style":872},[677,717],":",[573,2776,2778],{"className":2777},[576],[573,2779,2781,2864],{"className":2780},[580],[573,2782,2784],{"className":2783},[584],[586,2785,2786],{"xmlns":588,"display":589},[591,2787,2788,2861],{},[594,2789,2790,2796,2798,2804,2806,2808,2810,2813,2815,2817,2819,2821,2823,2826,2832,2834,2848,2850,2857,2859],{},[1467,2791,2792,2794],{},[603,2793,630],{},[616,2795,1871],{},[612,2797,627],{},[597,2799,2800,2802],{},[616,2801,2674],{},[616,2803,1882],{},[612,2805,627],{},[616,2807,2115],{},[632,2809],{"width":634},[612,2811,2812],{},"⇒",[632,2814],{"width":634},[603,2816,630],{},[612,2818,627],{},[616,2820,2059],{},[612,2822,1874],{"separator":644},[632,2824],{"width":2825},"2em",[600,2827,2828,2830],{},[603,2829,605],{},[616,2831,618],{},[612,2833,627],{},[597,2835,2836,2842],{},[600,2837,2838,2840],{},[603,2839,605],{},[616,2841,1871],{},[1467,2843,2844,2846],{},[603,2845,630],{},[616,2847,2059],{},[612,2849,627],{},[597,2851,2852,2854],{},[616,2853,1882],{},[616,2855,2856],{},"4",[612,2858,627],{},[616,2860,1871],{},[657,2862,2863],{"encoding":659},"q^3 = \\frac{96}{12} = 8 \\quad\\Rightarrow\\quad q = 2, \\qquad a_1 = \\frac{a_3}{q^2} = \\frac{12}{4} = 3",[573,2865,2867,2911,2991,3015,3033,3101,3245,3322],{"className":2866,"ariaHidden":644},[664],[573,2868,2870,2873,2902,2905,2908],{"className":2869},[668],[573,2871],{"className":2872,"style":2491},[672],[573,2874,2876,2879],{"className":2875},[677],[573,2877,630],{"className":2878,"style":872},[677,717],[573,2880,2882],{"className":2881},[721],[573,2883,2885],{"className":2884},[689],[573,2886,2888],{"className":2887},[694],[573,2889,2891],{"className":2890,"style":2228},[698],[573,2892,2893,2896],{"style":2249},[573,2894],{"className":2895,"style":738},[706],[573,2897,2899],{"className":2898},[742,743,744,745],[573,2900,1871],{"className":2901},[677,745],[573,2903],{"className":2904,"style":854},[632],[573,2906,627],{"className":2907},[858],[573,2909],{"className":2910,"style":854},[632],[573,2912,2914,2918,2982,2985,2988],{"className":2913},[668],[573,2915],{"className":2916,"style":2917},[672],"height:2.0074em;vertical-align:-0.686em;",[573,2919,2921,2924,2979],{"className":2920},[677],[573,2922],{"className":2923},[681,682],[573,2925,2927],{"className":2926},[597],[573,2928,2930,2970],{"className":2929},[689,690],[573,2931,2933,2967],{"className":2932},[694],[573,2934,2937,2948,2956],{"className":2935,"style":2936},[698],"height:1.3214em;",[573,2938,2939,2942],{"style":702},[573,2940],{"className":2941,"style":707},[706],[573,2943,2945],{"className":2944},[677],[573,2946,1882],{"className":2947},[677],[573,2949,2950,2953],{"style":765},[573,2951],{"className":2952,"style":707},[706],[573,2954],{"className":2955,"style":773},[772],[573,2957,2958,2961],{"style":776},[573,2959],{"className":2960,"style":707},[706],[573,2962,2964],{"className":2963},[677],[573,2965,2674],{"className":2966},[677],[573,2968,753],{"className":2969},[752],[573,2971,2973],{"className":2972},[694],[573,2974,2977],{"className":2975,"style":2976},[698],"height:0.686em;",[573,2978],{},[573,2980],{"className":2981},[850,682],[573,2983],{"className":2984,"style":854},[632],[573,2986,627],{"className":2987},[858],[573,2989],{"className":2990,"style":854},[632],[573,2992,2994,2997,3000,3003,3006,3009,3012],{"className":2993},[668],[573,2995],{"className":2996,"style":1044},[672],[573,2998,2115],{"className":2999},[677],[573,3001],{"className":3002,"style":876},[632],[573,3004],{"className":3005,"style":854},[632],[573,3007,2812],{"className":3008},[858],[573,3010],{"className":3011,"style":876},[632],[573,3013],{"className":3014,"style":854},[632],[573,3016,3018,3021,3024,3027,3030],{"className":3017},[668],[573,3019],{"className":3020,"style":954},[672],[573,3022,630],{"className":3023,"style":872},[677,717],[573,3025],{"className":3026,"style":854},[632],[573,3028,627],{"className":3029},[858],[573,3031],{"className":3032,"style":854},[632],[573,3034,3036,3039,3042,3045,3049,3052,3092,3095,3098],{"className":3035},[668],[573,3037],{"className":3038,"style":1905},[672],[573,3040,2059],{"className":3041},[677],[573,3043,1874],{"className":3044},[1912],[573,3046],{"className":3047,"style":3048},[632],"margin-right:2em;",[573,3050],{"className":3051,"style":1916},[632],[573,3053,3055,3058],{"className":3054},[677],[573,3056,605],{"className":3057},[677,717],[573,3059,3061],{"className":3060},[721],[573,3062,3064,3084],{"className":3063},[689,690],[573,3065,3067,3081],{"className":3066},[694],[573,3068,3070],{"className":3069,"style":801},[698],[573,3071,3072,3075],{"style":734},[573,3073],{"className":3074,"style":738},[706],[573,3076,3078],{"className":3077},[742,743,744,745],[573,3079,618],{"className":3080},[677,745],[573,3082,753],{"className":3083},[752],[573,3085,3087],{"className":3086},[694],[573,3088,3090],{"className":3089,"style":760},[698],[573,3091],{},[573,3093],{"className":3094,"style":854},[632],[573,3096,627],{"className":3097},[858],[573,3099],{"className":3100,"style":854},[632],[573,3102,3104,3108,3236,3239,3242],{"className":3103},[668],[573,3105],{"className":3106,"style":3107},[672],"height:1.988em;vertical-align:-0.8804em;",[573,3109,3111,3114,3233],{"className":3110},[677],[573,3112],{"className":3113},[681,682],[573,3115,3117],{"className":3116},[597],[573,3118,3120,3224],{"className":3119},[689,690],[573,3121,3123,3221],{"className":3122},[694],[573,3124,3126,3165,3173],{"className":3125,"style":699},[698],[573,3127,3128,3131],{"style":702},[573,3129],{"className":3130,"style":707},[706],[573,3132,3134],{"className":3133},[677],[573,3135,3137,3140],{"className":3136},[677],[573,3138,630],{"className":3139,"style":872},[677,717],[573,3141,3143],{"className":3142},[721],[573,3144,3146],{"className":3145},[689],[573,3147,3149],{"className":3148},[694],[573,3150,3153],{"className":3151,"style":3152},[698],"height:0.7401em;",[573,3154,3156,3159],{"style":3155},"top:-2.989em;margin-right:0.05em;",[573,3157],{"className":3158,"style":738},[706],[573,3160,3162],{"className":3161},[742,743,744,745],[573,3163,2059],{"className":3164},[677,745],[573,3166,3167,3170],{"style":765},[573,3168],{"className":3169,"style":707},[706],[573,3171],{"className":3172,"style":773},[772],[573,3174,3175,3178],{"style":776},[573,3176],{"className":3177,"style":707},[706],[573,3179,3181],{"className":3180},[677],[573,3182,3184,3187],{"className":3183},[677],[573,3185,605],{"className":3186},[677,717],[573,3188,3190],{"className":3189},[721],[573,3191,3193,3213],{"className":3192},[689,690],[573,3194,3196,3210],{"className":3195},[694],[573,3197,3199],{"className":3198,"style":801},[698],[573,3200,3201,3204],{"style":734},[573,3202],{"className":3203,"style":738},[706],[573,3205,3207],{"className":3206},[742,743,744,745],[573,3208,1871],{"className":3209},[677,745],[573,3211,753],{"className":3212},[752],[573,3214,3216],{"className":3215},[694],[573,3217,3219],{"className":3218,"style":760},[698],[573,3220],{},[573,3222,753],{"className":3223},[752],[573,3225,3227],{"className":3226},[694],[573,3228,3231],{"className":3229,"style":3230},[698],"height:0.8804em;",[573,3232],{},[573,3234],{"className":3235},[850,682],[573,3237],{"className":3238,"style":854},[632],[573,3240,627],{"className":3241},[858],[573,3243],{"className":3244,"style":854},[632],[573,3246,3248,3251,3313,3316,3319],{"className":3247},[668],[573,3249],{"className":3250,"style":2917},[672],[573,3252,3254,3257,3310],{"className":3253},[677],[573,3255],{"className":3256},[681,682],[573,3258,3260],{"className":3259},[597],[573,3261,3263,3302],{"className":3262},[689,690],[573,3264,3266,3299],{"className":3265},[694],[573,3267,3269,3280,3288],{"className":3268,"style":2936},[698],[573,3270,3271,3274],{"style":702},[573,3272],{"className":3273,"style":707},[706],[573,3275,3277],{"className":3276},[677],[573,3278,2856],{"className":3279},[677],[573,3281,3282,3285],{"style":765},[573,3283],{"className":3284,"style":707},[706],[573,3286],{"className":3287,"style":773},[772],[573,3289,3290,3293],{"style":776},[573,3291],{"className":3292,"style":707},[706],[573,3294,3296],{"className":3295},[677],[573,3297,1882],{"className":3298},[677],[573,3300,753],{"className":3301},[752],[573,3303,3305],{"className":3304},[694],[573,3306,3308],{"className":3307,"style":2976},[698],[573,3309],{},[573,3311],{"className":3312},[850,682],[573,3314],{"className":3315,"style":854},[632],[573,3317,627],{"className":3318},[858],[573,3320],{"className":3321,"style":854},[632],[573,3323,3325,3328],{"className":3324},[668],[573,3326],{"className":3327,"style":1044},[672],[573,3329,1871],{"className":3330},[677],[559,3332,3334],{"id":3333},"typische-fehler","Typische Fehler",[1111,3336,3337,3569,3670,3865],{},[1114,3338,3339,3462,3463,3568],{},[573,3340,3342,3368],{"className":3341},[580],[573,3343,3345],{"className":3344},[584],[586,3346,3347],{"xmlns":588},[591,3348,3349,3365],{},[594,3350,3351,3357,3359],{},[600,3352,3353,3355],{},[603,3354,605],{},[616,3356,618],{},[612,3358,1465],{},[1467,3360,3361,3363],{},[603,3362,630],{},[603,3364,610],{},[657,3366,3367],{"encoding":659},"a_1 \\cdot q^n",[573,3369,3371,3427],{"className":3370,"ariaHidden":644},[664],[573,3372,3374,3378,3418,3421,3424],{"className":3373},[668],[573,3375],{"className":3376,"style":3377},[672],"height:0.5945em;vertical-align:-0.15em;",[573,3379,3381,3384],{"className":3380},[677],[573,3382,605],{"className":3383},[677,717],[573,3385,3387],{"className":3386},[721],[573,3388,3390,3410],{"className":3389},[689,690],[573,3391,3393,3407],{"className":3392},[694],[573,3394,3396],{"className":3395,"style":801},[698],[573,3397,3398,3401],{"style":734},[573,3399],{"className":3400,"style":738},[706],[573,3402,3404],{"className":3403},[742,743,744,745],[573,3405,618],{"className":3406},[677,745],[573,3408,753],{"className":3409},[752],[573,3411,3413],{"className":3412},[694],[573,3414,3416],{"className":3415,"style":760},[698],[573,3417],{},[573,3419],{"className":3420,"style":1031},[632],[573,3422,1465],{"className":3423},[819],[573,3425],{"className":3426,"style":1031},[632],[573,3428,3430,3433],{"className":3429},[668],[573,3431],{"className":3432,"style":1672},[672],[573,3434,3436,3439],{"className":3435},[677],[573,3437,630],{"className":3438,"style":872},[677,717],[573,3440,3442],{"className":3441},[721],[573,3443,3445],{"className":3444},[689],[573,3446,3448],{"className":3447},[694],[573,3449,3451],{"className":3450,"style":1691},[698],[573,3452,3453,3456],{"style":1694},[573,3454],{"className":3455,"style":738},[706],[573,3457,3459],{"className":3458},[742,743,744,745],[573,3460,610],{"className":3461},[677,717,745]," rechnen. Im ersten Beispiel ergäbe das ",[573,3464,3466,3493],{"className":3465},[580],[573,3467,3469],{"className":3468},[584],[586,3470,3471],{"xmlns":588},[591,3472,3473,3490],{},[594,3474,3475,3477,3479,3485,3487],{},[616,3476,1871],{},[612,3478,1465],{},[1467,3480,3481,3483],{},[616,3482,2059],{},[616,3484,2115],{},[612,3486,627],{},[616,3488,3489],{},"768",[657,3491,3492],{"encoding":659},"3 \\cdot 2^8 = 768",[573,3494,3496,3514,3559],{"className":3495,"ariaHidden":644},[664],[573,3497,3499,3502,3505,3508,3511],{"className":3498},[668],[573,3500],{"className":3501,"style":1044},[672],[573,3503,1871],{"className":3504},[677],[573,3506],{"className":3507,"style":1031},[632],[573,3509,1465],{"className":3510},[819],[573,3512],{"className":3513,"style":1031},[632],[573,3515,3517,3521,3550,3553,3556],{"className":3516},[668],[573,3518],{"className":3519,"style":3520},[672],"height:0.8141em;",[573,3522,3524,3527],{"className":3523},[677],[573,3525,2059],{"className":3526},[677],[573,3528,3530],{"className":3529},[721],[573,3531,3533],{"className":3532},[689],[573,3534,3536],{"className":3535},[694],[573,3537,3539],{"className":3538,"style":3520},[698],[573,3540,3541,3544],{"style":1694},[573,3542],{"className":3543,"style":738},[706],[573,3545,3547],{"className":3546},[742,743,744,745],[573,3548,2115],{"className":3549},[677,745],[573,3551],{"className":3552,"style":854},[632],[573,3554,627],{"className":3555},[858],[573,3557],{"className":3558,"style":854},[632],[573,3560,3562,3565],{"className":3561},[668],[573,3563],{"className":3564,"style":1044},[672],[573,3566,3489],{"className":3567},[677],", doppelt so viel wie richtig.",[1114,3570,3571,3572,3640,3641,3669],{},"Arithmetisch und geometrisch verwechseln: Bei ",[573,3573,3575,3601],{"className":3574},[580],[573,3576,3578],{"className":3577},[584],[586,3579,3580],{"xmlns":588},[591,3581,3582,3598],{},[594,3583,3584,3586,3588,3590,3592,3594,3596],{},[616,3585,1871],{},[612,3587,1874],{"separator":644},[616,3589,1877],{},[612,3591,1874],{"separator":644},[616,3593,1882],{},[612,3595,1874],{"separator":644},[612,3597,1892],{},[657,3599,3600],{"encoding":659},"3, 6, 12, \\ldots",[573,3602,3604],{"className":3603,"ariaHidden":644},[664],[573,3605,3607,3610,3613,3616,3619,3622,3625,3628,3631,3634,3637],{"className":3606},[668],[573,3608],{"className":3609,"style":1905},[672],[573,3611,1871],{"className":3612},[677],[573,3614,1874],{"className":3615},[1912],[573,3617],{"className":3618,"style":1916},[632],[573,3620,1877],{"className":3621},[677],[573,3623,1874],{"className":3624},[1912],[573,3626],{"className":3627,"style":1916},[632],[573,3629,1882],{"className":3630},[677],[573,3632,1874],{"className":3633},[1912],[573,3635],{"className":3636,"style":1916},[632],[573,3638,1892],{"className":3639},[1947]," wird nicht immer ",[573,3642,3644,3657],{"className":3643},[580],[573,3645,3647],{"className":3646},[584],[586,3648,3649],{"xmlns":588},[591,3650,3651,3655],{},[594,3652,3653],{},[616,3654,1871],{},[657,3656,1871],{"encoding":659},[573,3658,3660],{"className":3659,"ariaHidden":644},[664],[573,3661,3663,3666],{"className":3662},[668],[573,3664],{"className":3665,"style":1044},[672],[573,3667,1871],{"className":3668},[677]," addiert, sondern verdoppelt.",[1114,3671,3672,3673,3755,3756,3806,3807,3864],{},"Bei geradem Exponenten nur die positive Lösung beachten: Aus ",[573,3674,3676,3698],{"className":3675},[580],[573,3677,3679],{"className":3678},[584],[586,3680,3681],{"xmlns":588},[591,3682,3683,3695],{},[594,3684,3685,3691,3693],{},[1467,3686,3687,3689],{},[603,3688,630],{},[616,3690,2059],{},[612,3692,627],{},[616,3694,2856],{},[657,3696,3697],{"encoding":659},"q^2 = 4",[573,3699,3701,3746],{"className":3700,"ariaHidden":644},[664],[573,3702,3704,3708,3737,3740,3743],{"className":3703},[668],[573,3705],{"className":3706,"style":3707},[672],"height:1.0085em;vertical-align:-0.1944em;",[573,3709,3711,3714],{"className":3710},[677],[573,3712,630],{"className":3713,"style":872},[677,717],[573,3715,3717],{"className":3716},[721],[573,3718,3720],{"className":3719},[689],[573,3721,3723],{"className":3722},[694],[573,3724,3726],{"className":3725,"style":3520},[698],[573,3727,3728,3731],{"style":1694},[573,3729],{"className":3730,"style":738},[706],[573,3732,3734],{"className":3733},[742,743,744,745],[573,3735,2059],{"className":3736},[677,745],[573,3738],{"className":3739,"style":854},[632],[573,3741,627],{"className":3742},[858],[573,3744],{"className":3745,"style":854},[632],[573,3747,3749,3752],{"className":3748},[668],[573,3750],{"className":3751,"style":1044},[672],[573,3753,2856],{"className":3754},[677]," folgt ",[573,3757,3759,3776],{"className":3758},[580],[573,3760,3762],{"className":3761},[584],[586,3763,3764],{"xmlns":588},[591,3765,3766,3774],{},[594,3767,3768,3770,3772],{},[603,3769,630],{},[612,3771,627],{},[616,3773,2059],{},[657,3775,2062],{"encoding":659},[573,3777,3779,3797],{"className":3778,"ariaHidden":644},[664],[573,3780,3782,3785,3788,3791,3794],{"className":3781},[668],[573,3783],{"className":3784,"style":954},[672],[573,3786,630],{"className":3787,"style":872},[677,717],[573,3789],{"className":3790,"style":854},[632],[573,3792,627],{"className":3793},[858],[573,3795],{"className":3796,"style":854},[632],[573,3798,3800,3803],{"className":3799},[668],[573,3801],{"className":3802,"style":1044},[672],[573,3804,2059],{"className":3805},[677]," oder ",[573,3808,3810,3830],{"className":3809},[580],[573,3811,3813],{"className":3812},[584],[586,3814,3815],{"xmlns":588},[591,3816,3817,3827],{},[594,3818,3819,3821,3823,3825],{},[603,3820,630],{},[612,3822,627],{},[612,3824,1009],{},[616,3826,2059],{},[657,3828,3829],{"encoding":659},"q = -2",[573,3831,3833,3851],{"className":3832,"ariaHidden":644},[664],[573,3834,3836,3839,3842,3845,3848],{"className":3835},[668],[573,3837],{"className":3838,"style":954},[672],[573,3840,630],{"className":3841,"style":872},[677,717],[573,3843],{"className":3844,"style":854},[632],[573,3846,627],{"className":3847},[858],[573,3849],{"className":3850,"style":854},[632],[573,3852,3854,3858,3861],{"className":3853},[668],[573,3855],{"className":3856,"style":3857},[672],"height:0.7278em;vertical-align:-0.0833em;",[573,3859,1009],{"className":3860},[677],[573,3862,2059],{"className":3863},[677],".",[1114,3866,3867,3868,3938,3939,4009,4010,3864],{},"Die Formel mit ",[573,3869,3871,3889],{"className":3870},[580],[573,3872,3874],{"className":3873},[584],[586,3875,3876],{"xmlns":588},[591,3877,3878,3886],{},[594,3879,3880],{},[600,3881,3882,3884],{},[603,3883,605],{},[616,3885,618],{},[657,3887,3888],{"encoding":659},"a_1",[573,3890,3892],{"className":3891,"ariaHidden":644},[664],[573,3893,3895,3898],{"className":3894},[668],[573,3896],{"className":3897,"style":1485},[672],[573,3899,3901,3904],{"className":3900},[677],[573,3902,605],{"className":3903},[677,717],[573,3905,3907],{"className":3906},[721],[573,3908,3910,3930],{"className":3909},[689,690],[573,3911,3913,3927],{"className":3912},[694],[573,3914,3916],{"className":3915,"style":801},[698],[573,3917,3918,3921],{"style":734},[573,3919],{"className":3920,"style":738},[706],[573,3922,3924],{"className":3923},[742,743,744,745],[573,3925,618],{"className":3926},[677,745],[573,3928,753],{"className":3929},[752],[573,3931,3933],{"className":3932},[694],[573,3934,3936],{"className":3935,"style":760},[698],[573,3937],{}," benutzen, obwohl die Folge bei ",[573,3940,3942,3960],{"className":3941},[580],[573,3943,3945],{"className":3944},[584],[586,3946,3947],{"xmlns":588},[591,3948,3949,3957],{},[594,3950,3951],{},[600,3952,3953,3955],{},[603,3954,605],{},[616,3956,1192],{},[657,3958,3959],{"encoding":659},"a_0",[573,3961,3963],{"className":3962,"ariaHidden":644},[664],[573,3964,3966,3969],{"className":3965},[668],[573,3967],{"className":3968,"style":1485},[672],[573,3970,3972,3975],{"className":3971},[677],[573,3973,605],{"className":3974},[677,717],[573,3976,3978],{"className":3977},[721],[573,3979,3981,4001],{"className":3980},[689,690],[573,3982,3984,3998],{"className":3983},[694],[573,3985,3987],{"className":3986,"style":801},[698],[573,3988,3989,3992],{"style":734},[573,3990],{"className":3991,"style":738},[706],[573,3993,3995],{"className":3994},[742,743,744,745],[573,3996,1192],{"className":3997},[677,745],[573,3999,753],{"className":4000},[752],[573,4002,4004],{"className":4003},[694],[573,4005,4007],{"className":4006,"style":760},[698],[573,4008],{}," beginnt. Dann gilt ",[573,4011,4013,4047],{"className":4012},[580],[573,4014,4016],{"className":4015},[584],[586,4017,4018],{"xmlns":588},[591,4019,4020,4044],{},[594,4021,4022,4028,4030,4036,4038],{},[600,4023,4024,4026],{},[603,4025,605],{},[603,4027,610],{},[612,4029,627],{},[600,4031,4032,4034],{},[603,4033,605],{},[616,4035,1192],{},[612,4037,1465],{},[1467,4039,4040,4042],{},[603,4041,630],{},[603,4043,610],{},[657,4045,4046],{"encoding":659},"a_n = a_0 \\cdot 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class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\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>q\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">q \\neq 0,\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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\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>\u003Cmi mathvariant=\"double-struck\">N\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\in \\mathbb{N},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">N\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\geq 1\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","geometric-sequence","a_n = a_1 \\cdot q^{n - 1}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsup>\u003Cmi>q\u003C\u002Fmi>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a_n = a_1 \\cdot q^{n - 1}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.5945em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\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:1.0585em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8641em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003Cspan class=\"mbin mtight\">−\u003C\u002Fspan>\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fgeometrische-folge",[],[4240,4241,4242,4243],"geometric-sum","arithmetic-sequence","exponential-function","compound-interest",{"title":548,"description":4196},"de\u002Fformulas\u002Fmath\u002Fsequences-series\u002Fgeometrische-folge","In einer geometrischen Folge entsteht jedes Glied durch Multiplikation mit demselben Faktor q, also a₁ · qⁿ⁻¹.",[4248,4249,4250,4251,4252],"folge","geometrische folge","quotient","explizite darstellung","rekursion",[4254,4258,4261,4264],{"symbol":4255,"meaning":4256,"symbolHtml":4257},"a_n","n-tes Glied der Folge","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a_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:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" 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