Konvergenz von Reihen

Konvergenz von Reihen Eine Reihe konvergiert gegen S, falls gilt: lim n → ∞ s n = lim n → ∞ ( ∑ i = 0 n a i ) = S MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfgBPj MCPbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8XjY=vipgYlh9vqqj=hEeeu0xXdbb a9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yq aiVgFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabaqaamaaeaqbaaGcba WaaCbeaeaaciGGSbGaaiyAaiaac2gaaSqaaiaad6gacqGHsgIRcqGH EisPaeqaaOGaaeiiaiaadohadaWgaaWcbaGaamOBaaqabaGccqGH9a qpdaWfqaqaaiGacYgacaGGPbGaaiyBaaWcbaGaamOBaiabgkziUkab g6HiLcqabaGcdaqadaqaamaaqahabaGaamyyamaaBaaaleaacaWGPb aabeaaaeaacaWGPbGaeyypa0JaaGimaaqaaiaad6gaa0GaeyyeIuoa aOGaayjkaiaawMcaaiabg2da9iaadofaaaa@5681@ Beispiel : a n = 1 n 2 ⇒ lim n → ∞ s n = lim n → ∞ ( ∑ i = 0 n a i ) = lim n → ∞ ( ∑ i = 1 n 1 n 2 ) = 1 + 1 4 + 1 9 + 1 16 + ... = π 2 6 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfgBPj MCPbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1B TfMBaebbnrfifHhDYfgasaacH8XjY=vipgYlh9vqqj=hEeeu0xXdbb a9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yq aiVgFr0xfr=xfr=xb9adbaqaaeaacaGaaiaabaqaamaaeaqbaaGcea qabeaacaWGHbWaaSbaaSqaaiaad6gaaeqaaOGaeyypa0ZaaSaaaeaa caaIXaaabaGaamOBamaaCaaaleqabaGaaGOmaaaaaaaakeaacqGHsh I3daWfqaqaaiGacYgacaGGPbGaaiyBaaWcbaGaamOBaiabgkziUkab g6HiLcqabaGccaqGGaGaam4CamaaBaaaleaacaWGUbaabeaakiabg2 da9maaxababaGaciiBaiaacMgacaGGTbaaleaacaWGUbGaeyOKH4Qa eyOhIukabeaakmaabmaabaWaaabCaeaacaWGHbWaaSbaaSqaaiaadM gaaeqaaaq