구 lim [x ^ (n + 1) - (n + 1) x + n] / (x - 1) ^ 2 x - > 1

구 lim [x ^ (n + 1) - (n + 1) x + n] / (x - 1) ^ 2 x - > 1

영: 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