Question

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

Answer 1

Sn=a1n+n(n-1)d/2
S2n=2a1n+n(2n-1)d
S3n=3a1n+3n(3n-1)d/2
S2n-Sn-Sn=2a1n+n(2n-1)d-2a1n+n(n-1)d=n^2d
S3n-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成等差数列
如果本题有什么不明白可以追问，如果满意记得采纳
如果有其他问题请另发或点击向我求助，答题不易，请谅解，谢谢。
祝学习进步！

Answer 2