一道关于极限的题目

原式=（n^2+2n）^(1/2)-n=[(n^2+2n)^(1/2)-n]*[(n^2+2n)^(1/2)+n]/[(n^2+2n)^(1/2)+n]
=(n^2+2n-n^2)/[(n^2+2n)^(1/2)+n]
=2n/[(n^2+2n)^(1/2)+n]
=2/{[(n^2+2n)^(1/2)+n]/n}
=2/[[(n^2+2n)/(n^2)]^(1/2)+1]
=2/[(2/n+1)^(1/2)+1]
求极限后就是:2/2=1

lim 根号(n²+2n)-n
=lim 2n/[根号(n²+2n)+n]
=lim 2/[根号(1+2/n)+1]
=2/[根号(1+0)+1]
=1

把n提出来就行了