1/2^2+1/3^2+....+1/n^2>1/(2*3)+1/(3*4)+...+1/[n*(n+1)]
而: 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)
1/2^2+1/3^2+....+1/n^2<1/(1*2)+1/(2*3)+...+1/[(n-1)*n]
而: 1/(1*2)+1/(2*3)+...+1/[(n-1)*n]
=1-1/2+1/2-1/3+...+1/(n-1)-1/n
=1-1/n
所以,得证.
注:你要证的左边是"1/2-1/(n+1)"吧.