求极限 lim【1/(n^2+n+1)+2/(n^2+n+2)+3/(n^2+n+3)+……+n/(n^2+n+n)】n趋向于无穷

问题描述:

求极限 lim【1/(n^2+n+1)+2/(n^2+n+2)+3/(n^2+n+3)+……+n/(n^2+n+n)】n趋向于无穷

答案是1/2
使用夹逼法.
分母都换成n^2+n+1求出极限为1/2
分母都换成n^2+n+n求出极限也为1/2
根据夹逼准则 得出极限为1/2