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JEE Main202127 Jul 2021Morning ShiftMathematicsDefinite IntegrationActual

The value of lim n → ∞ 1 n ∑ j = 1 n 2 j - 1 + 8 n 2 j - 1 + 4 n is equal to:

Options

  1. A5 + log e 3 2
  2. B2 - log e 2 3
  3. C3 + 2 log e 2 3
  4. D1 + 2 log e 3 2

Correct answer

D. 1 + 2 log e 3 2

Step-by-step solution

lim n → ∞ 1 n ∑ j = 1 n 2 j n - 1 n + 8 2 j n - 1 n + 4 ∫ 0 1 2 x + 8 2 x + 4 d x = ∫ 0 1 d x + ∫ 0 1 4 2 x + 4 d x = 1 + 4 1 2 l n 2 x + 4 | 0 1 = 1 + 2 ℓ n 3 2

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