问题描述: 设Sn是等差数列{an}的前n项和,求证:若正整数m,n,p成等差数列,则Sm/m,Sn/n,Sp/p也成等差数列. 1个回答 分类:数学 2014-10-25 问题解答: 我来补答 Sn=[(a1+a1+(n-1)d]*n/2=[2a1+(n-1)d)]*n/2Sm/m={[2a1+(m-1)d)]*m/2}/m=a1+(m-1)d/2Sn/n=a1+(n-1)d/2Sp/p=a1+(p-1)d/22Sn/n=2a1+(n-1)dm,n,p成等差数列,2n=m+p(Sm/m)+(Sp/p)=a1+(m-1)d/2+a1+(p-1)d/2=2a1+(m+p-2)d/2=2a1+(2n-2)d/2=2a1+(n-1)d2Sn/n=(Sm/m)+(Sp/p)Sm/m,Sn/n,Sp/p也成等差数列 展开全文阅读