若數(shù)列{An}的前n項(xiàng)和Sn=2An+1,問數(shù)列{An}是否成等比數(shù)列?說明理由,并求出An
熱心網(wǎng)友
Sn=2An+1 == Sn-1 =2A(n-1)+1 == Sn - Sn-1 = An = (2An+1)-[2A(n-1)+1] = 2An -2A(n-1)An/A(n-1) = 2== {An}成等比數(shù)列S1 = A1 = 2A1 +1 == A1 = -1== An = 1 - 2^n
若數(shù)列{An}的前n項(xiàng)和Sn=2An+1,問數(shù)列{An}是否成等比數(shù)列?說明理由,并求出An
Sn=2An+1 == Sn-1 =2A(n-1)+1 == Sn - Sn-1 = An = (2An+1)-[2A(n-1)+1] = 2An -2A(n-1)An/A(n-1) = 2== {An}成等比數(shù)列S1 = A1 = 2A1 +1 == A1 = -1== An = 1 - 2^n