若数列{an}的前n项之和为Sn,且满足lg (Sn+1)=n,求证:数列{an}是等比数列.

问题描述:

若数列{an}的前n项之和为Sn,且满足lg (Sn+1)=n,求证:数列{an}是等比数列.

∵lg (Sn+1)=n,
∴sn+1=10n
∴sn=10n-1,
∴数列前n项和满足等比数列的公式,
∴数列是等比数列.