用放缩法证明:1/2-1/(n+1)
问题描述：
用放缩法证明:1/2-1/(n+1)
答
1/(2^2)+1/(3^2)+````+1/(n^2)
=1-1/2+1/2+1/3+……+1/(n-1)-1/n
=1-1/n=(n-1)/n;
1/(2^2)+1/(3^2)+````+1/(n^2)
>1/(2*3)+1/(3*4)+````+1/[n*(n+1)]
=1/2-1/3+1/3-1/4……+1/n-1/(n+1)
=1/2-1/(n+1)
答
估计你题目打错了.我自己改一下.把3^3改成3^2
1/(2^2)+1/(3^2)+````+1/(n^2)
> 1/(2*3)+1/(3*4)+.+1/[n(n+1)]
=1/2-1/3+1/3-1/4+.+1/n-1/(n+1)
=1/2-1/(n+1)
右半部分
1/(2^2)+1/(3^2)+````+1/(n^2)
=1-1/2+1/2-1/3.+1/(n-1)-1/n
=(n-1)/n