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The value of l i m n → ∞ ∑ r = 1 n 2 r + 3 r 6 r is equal to

Options

  1. A0
  2. B1
  3. C6
  4. D3 2

Correct answer

D. 3 2

Step-by-step solution

l i m n → ∞ ∑ r = 1 n 2 r 6 r + 3 r 6 r ⇒ l i m n → ∞ ∑ r = 1 n 1 3 r + 1 2 r ⇒ l i m n → ∞ 1 3 1 - 1 3 n 1 - 1 3 + 1 2 1 - 1 2 n 1 - 1 2 ⇒ 1 3 1 - 0 2 3 + 1 2 1 - 0 1 2 ⇒ 1 2 + 1 = 3 2

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