我只写主体部分了假设 1/(2*2) +1/(3*3)............+1/(n*n)<(n-1)/n则1/(2*2) +1/(3*3)............+1/(n*n)+1/(n+1)(n+1)<(n-1)/n + 1/(n+1)(n+1)<(n-1)/n + 1/n(n+1)=(n*n)/n(n+1)=n/(n+1)得证
