因为[1/(根号下n^2+1)+1/(根号下n^2+2).+1/(根号下n^2+n)]小于n/(根号下n^2+1)+1 [1/(根号下n^2+1)+1/(根号下n^2+2).+1/(根号下n^2+n)]大于n/(根号下n^2+n) 因为n/(根号下n^2+1)+1 的极限为1 n/(根号下n^2+n)的极限也为1 所以lim n→∞[1/(根号下n^2+1)+1/(根号下n^2+2).+1/(根号下n^2+n)]=1