已知函数f(x)=x^2+bx为偶函数,数列{an}满足an+1=2f(an-1)+1,且a1=3,an>1.(1)bn=log(an-1),求证:数列{bn+1}为等比数列;(2)cn=nbn,求数列{cn}的前n项和sn

问题描述:

已知函数f(x)=x^2+bx为偶函数,数列{an}满足an+1=2f(an-1)+1,且a1=3,an>1.
(1)bn=log(an-1),求证:数列{bn+1}为等比数列;
(2)cn=nbn,求数列{cn}的前n项和sn