Geometrische Reihe

Geometrische Reihen sind Reihen der Form s n = ∑ k = 0 n a ⋅ q k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfgBPj MCPbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8XjY=vipgYlh9vqqj=hEeeu0xXdbb a9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yq aiVgFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabaqaamaaeaqbaaGcba Gaam4CamaaBaaaleaacaWGUbaabeaakiabg2da9maaqahabaGaamyy aiabgwSixlaadghadaahaaWcbeqaaiaadUgaaaaabaGaam4Aaiabg2 da9iaaicdaaeaacaWGUbaaniabggHiLdaaaa@46EA@ . Geometrische Reihen gibt es in endlicher oder unendlicher Form. Die endlichen geometrischen Reihen lassen sich berechnen durch s n = a ⋅ ( 1 − q n + 1 1 − q ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfgBPj MCPbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8XjY=vipgYlh9vqqj=hEeeu0xXdbb a9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yq aiVgFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabaqaamaaeaqbaaGcba Gaam4CamaaBaaaleaacaWGUbaabeaakiabg2da9iaadggacqGHflY1 daqadaqaamaalaaabaGaaGymaiabgkHiTiaadghadaahaaWcbeqaai aad6gacqGHRaWkcaaIXaaaaaGcbaGaaGymaiabgkHiTiaadghaaaaa caGLOaGaayzkaaaaaa@4899@ . Beispiel: s n = ∑ k = 0 n 3 ⋅ 2 k s 1 = 3 ⋅ 2 0 + 3 ⋅ 2 1 = 3 ⋅ 1 + 3 ⋅ 2 = 9 s 1 = 3 ⋅ ( 1 − 2 2 1 − 2 ) = 3 ⋅ 3 = 9 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfgBPj MCPbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8XjY=vipgYlh9vqqj=hEeeu0xXdbb a9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc