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The limit L = lim n → ∞ ⁡ ∑ r = 1 n n n 2 + r 2 satisfies

Options

  1. Aπ L > 6
  2. Bπ L < 2
  3. Cπ L > 3
  4. Dπ L < 1

Correct answer

C. π L > 3

Step-by-step solution

Given limit is L = lim n &#x2192; &#x221E; &#x2211; r = 1 n 1 1 + r n 2 &#x22C5; 1 n = ∫ 0 1 d x 1 + x 2 = tan - 1 ⁡ x 0 1 = π 4

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