k/n-1/n+1-1/n+2-....-1/n+k=(1/n-1/(n+1))+...+(1/n-1/(n+k)）而（1/n-1/(n+i))*n^2=i/(1+i/n)。当n趋于无穷时极限为i所以原式=1+2+。。。+k=k(k+1)/2
