各项和为正数的数列an和bn满足an,bn,an+1成等差数列,bn,an+1,bn+1成等比数列 求证（根号bn）是等差数列
问题描述：
各项和为正数的数列an和bn满足an,bn,an+1成等差数列,bn,an+1,bn+1成等比数列 求证（根号bn）是等差数列
答
题意：an+an+1=2bn; (1) bnbn+1=an+1*an+1 (2)（2）式两边开方得：an+1=sqrt(bn)*sqrt(bn+1) (3)(1)式两边平方,展开,然后将（3）式代入,可得：bn*bn-1+bn*bn+1+2*sqrt(bn-1*bn*bn*bn+1)=4bn*bn (4)整理（4）式后可得...