（1）当n=2时,1/2^2=1/4<(2-1)/2=1/2,不等式成立.
（2）假设当n=k(k>=2)时不等时成立,那么,对于n=k+1,有
1/2^2+a/3^2+……+1/k^2+1/(k+1)^2<(k-1)/k+1/(k+1)^2=(k^3+k^2-1)/k(k+1)^2<=(k^3+k^2)/k(k+1)^2=k/(k+1).故当n=k+1时不等式也成立.
综上所述,不等式成立.