k/(n^2+n+1)>=k/(n^2+n+k)>=k/(n^2+n+n)分别在[1,n]上求和得(n+1)n/2(n^2+n+1)>=S>=(n+1)n/2(n^2+n+n)在n趋向于无穷大的时候取极限得1/2>=S>=1/2所以所求极限为1/2
