等比数列之和怎么算_生活经验

q≠1时,Sn=a1(1-q^n)/(1-q)=(a1-anq)/(1-q)，q=1时Sn=na1 。(a1为首项，an为第n项，d为公差，q为等比)
证明过程
等比数列前n项和Sn=a1 a2 ... an=a1(1-q^n)/(1-q)
(公比q≠1)
证：Sn=a1 a1q a1q^2... a1q^(n-1)...........(1)
qSn=a1q a1q^2 ....a1q^(n-1) a1q^n.......(2)
(1)-(2):
(1-q)Sn=a1-a1q^n
【等比数列之和怎么算】∴Sn=a1(1-q^n)/(1-q)