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NTA Abhyas JEE Main2020MathematicsLimitsPractice

The value of l i m n → ∞ 1 2 - 2 2 + 3 2 - 4 2 + 5 2 . . . . + 2 n + 1 2 n 2 is equal to

Options

  1. A2
  2. B4
  3. C6
  4. D8

Correct answer

A. 2

Step-by-step solution

l i m n → ∞ 1 2 + 3 + 2 3 - 2 + . . . . . . . 2 n + 1 - 2 n 2 n + 1 + 2 n n 2 = l i m n → ∞ 1 + 2 + 3 + 4 + 5 + . . . . + 2 n + 1 n 2 = lim n → ∞ 2 n + 1 2 n + 2 2 n 2 = l i m n → ∞ n 2 2 + 1 n 2 + 2 n 2 n 2 = 2 × 2 2 = 2

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