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NTA Abhyas JEE Main2020MathematicsDefinite IntegrationPractice

If the value of the limit lim n → ∞ ⁡ 1 10 + 2 10 + … + n 10 n 11 is equal to K , then the value of 1 2 K is equal to (where, . represents the greatest integer function)

Options

  1. A4
  2. B5
  3. C10
  4. D11

Correct answer

B. 5

Step-by-step solution

The given limit is K = l i m n → ∞ ∑ r = 1 n r 10 n 11 = l i m n → ∞ ∑ r = 1 n r n 10 1 n = ∫ 0 1 x 10 d x = x 11 11 1 0 = 1 11 ⇒ 1 2 K = 11 2 ⇒ 1 2 K = 11 2 = 5.5 = 5

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