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The value of l i m n → ∞ e 1 n n 2 + 2 e 2 n n 2 + 3 e 3 n n 2 + … + 2 e 2 n is

Options

  1. Ae 2 - 1
  2. Be 2 + 1
  3. C2 e 2 + 1
  4. D2 e 2 - 1

Correct answer

B. e 2 + 1

Step-by-step solution

Let, I = l i m n → ∞   ∑ r = 1 2 n r n 2 e r n I = l i m n → ∞   ∑ r = 1 2 n r n e r n 1 n I = ∫ 0 2 x e x d x I = x e x 0 2 - ∫ 0 2 e x d x I = 2 e 2 - e 2 - 1 I = e 2 + 1

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