已知等差数列｛an｝的前n项和为Sn,公差为d.
问题描述：
已知等差数列｛an｝的前n项和为Sn,公差为d.
求证：Sn,S2n-Sn,S3n-S2n,.成等差数列
答
Sn=a1n+n(n-1)d/2S2n=2a1n+n(2n-1)dS3n=3a1n+3n(3n-1)d/2S2n-Sn-Sn=2a1n+n(2n-1)d-2a1n+n(n-1)d=n^2dS3n-S2n-(S2n-Sn)=S3n-2S2n+Sn=3a1n+3n(3n-1)d/2-4a1n-2n(2n-1)d+a1n+n(n-1)d/2=n^2d所以,Sn,S2n-Sn,S3n-S2n成等...