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The sum of infinite terms of the sequence whose r t h term is given by t r = 1 r + 1 r + 3 is equal to

Options

  1. A1
  2. B2
  3. C3 4
  4. D5 12

Correct answer

D. 5 12

Step-by-step solution

t r = 1 2 r + 3 - r + 1 r + 1 r + 3 = 1 2 1 r + 1 - 1 r + 3 ∑ r = 1 ∞ t r = 1 2 ∑ r = 1 ∞ 1 r + 1 - 1 r + 3 = 1 2 1 2 - 1 4 + 1 3 - 1 5 + 1 4 - 1 6 + . … … . = 1 2 1 2 + 1 3 = 5 12 .

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