lim n → ∞ 1 2 n 1 1 - 1 2 n + 1 1 - 2 2 n + 1 1 - 3 2 n + … . + 1 1 - 2 n - 1 2 n is equal to

Step-by-step solution

Let I = lim n → ∞ 1 2 n 1 1 - 1 2 n + 1 1 - 2 2 n + 1 1 - 3 2 n + … . + 1 1 - 2 n - 1 2 n Let 2 n = t and if n → ∞ then t → ∞ I = lim n → ∞ 1 t ∑ r = 1 t - 1 1 1 - r t I = ∫ 0 1 d x 1 - x (Using definite integral as limit of sum) Applying ∫ 0 a f x d x = ∫ 0 a f a - x d x , we get I = ∫ 0 1 d x x   = 2 x 0 1 = 2