等比数列前n项,前2n项,前3n项的和分别是Sn,S2n,S3n,求证Sn,S2n-Sn,S3n-S2n也成等比数列

问题描述:

等比数列前n项,前2n项,前3n项的和分别是Sn,S2n,S3n,求证Sn,S2n-Sn,S3n-S2n也成等比数列

Sn=a1(1-q^n)/(1-q)
S2n=a1(1-q^2n)/(1-q)
S3n=a1(1-q^3n)/(1-q)
(S2n-Sn)/Sn=q^n
(S3n-S2n)/S2n-Sn=q^n
所以这三者成等比数列