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The sum to the infinite terms of the series 5 3 2 ⋅ 7 2 + 9 7 2 ⋅ 1 1 2 + 13 1 1 2 ⋅ 1 5 2 + . . . . is

Options

  1. A1 8
  2. B1 36
  3. C1 54
  4. D1 72

Correct answer

D. 1 72

Step-by-step solution

T k = 5 + k - 1 4 3 + k - 1 4 2 7 + k - 1 4 2 = 4 k + 1 4 k - 1 2 4 k + 3 2 = 1 8 1 4 k - 1 2 - 1 4 k + 3 2 S n = T 1 + T 2 + T 3 + . . . . + T n = 1 8 1 3 2 - 1 7 2 + 1 7 2 - 1 1 1 2 + 1 1 1 2 - 1 1 5 2 + . . . . + 1 4 n - 1 2 - 1 4 n + 3 2 = 1 8 1 3 2 - 1 4 n + 3 2 S ∞ = l i m n → ∞ S n = 1 8 1 9 - 0 = 1 72

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