求lim[ x^(n+1)-(n+1)x+n]/(x-1)^2 x-->1
问题描述：
求lim[ x^(n+1)-(n+1)x+n]/(x-1)^2 x-->1
答
令：x = 1+t (t->0)
lim(x->1) [ x^(n+1)-(n+1)x+n]/(x-1)^2
=lim(t->0) [ (1+t)^(n+1)-(n+1)(1+t) + n]/t^2
=lim(t->0) [ [ 1 + (n+1)t + (n+1)n/2t^2 + o(t^2)] -(n+1)-(n+1)t + n]/t^2
=(n+1)n/2