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AP EAMCET201921 Apr 2019Evening ShiftMathematicsDefinite IntegrationActual

lim n → ∞ 1 + 2 + … + n n 3 2 =

Options

  1. A0
  2. B2 3
  3. C1
  4. D3 2

Correct answer

B. 2 3

Step-by-step solution

The expression is given as, I = lim n → ∞ 1 + 2 + … . + n n 3 2 = lim n → ∞ 1 + 2 + … . . + n n n = lim n → ∞ 1 n 1 n + 2 n + … + n n = ∑ r = 1 n lim n → ∞ 1 n 1 n = ∫ 0 1 x d x = 2 3 x 3 2 0 1 = 2 3

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