2n/(n+1)和2^(n+1)/n^2比较大小?

题目

2n/(n+1)和2^(n+1)/n^2比较大小?
n为正整数
能不能作差比较？

答案

当n=1时2n/(n+1)=1,2^(n+1)/n^2=4,2^(n+1)/n^2>2^(n+1)/n^2当n=2时2n/(n+1)=4/3,2^(n+1)/n^2=2,2^(n+1)/n^2>2^(n+1)/n^2当n=3时2n/(n+1)=6/4,2^(n+1)/n^2=16/9,2^(n+1)/n^2>2^(n+1)/n^2当n>3时,2n/(n+1)=2-2/(n+1)...