在等比数列{an}(n∈N*)中,a1>1,公比q>0.设bn=log2an,且b1+b3+b5=6,b1b3b5=0.(1)求证:数列{bn}是等差数列;(2)求{bn}的前n项和Sn及{an}的通项an;(3)试比较an与Sn的大小
问题描述:
在等比数列{an}(n∈N*)中,a1>1,公比q>0.设bn=log2an,且b1+b3+b5=6,b1b3b5=0.
(1)求证:数列{bn}是等差数列;
(2)求{bn}的前n项和Sn及{an}的通项an;
(3)试比较an与Sn的大小
答
1.证:b1+b3+b5=log2(a1)+log2(a3)+log2(a5)=log2(a1a3a5)=log2[(a3/q²)a3(a3q²)]=log2(a3³)=3log2(a3)=6log2(a3)=2a3=4b1b3b5=0log2(a1)×log2(a3)×log2(a5)=0log2(a1),log2(a3),log2(a5)中至少有...