已知数列{an}的通项公式an=log2[(n+1)/(n+2)](n∈N),设其前n项的和为Sn,则使Sn

题目

已知数列{an}的通项公式an=log2[(n+1)/(n+2)](n∈N),设其前n项的和为Sn,则使Sn

答案

an=log2(n+1)-log2(n+2)
Sn=log2(2)-log2(3)+log2(3)-log2(4)+.+log2(n)-log2(n+1)+log2(n+1)-log2(n+2)
=log2(2)-log2(n+2)
=1-log2(n+2)
6
∴n+2>64
∴n>62
选A