Find Lim [x ^ (n + 1) - (n + 1) x + n] / (x-1) ^ 2 x -- > 1

Find Lim [x ^ (n + 1) - (n + 1) x + n] / (x-1) ^ 2 x -- > 1

Let: 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