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The sum of the first 20 terms of the series 1 + 3 2 + 7 4 + 15 8 + 31 16 + … is

Options

  1. A39 + 1 2 19
  2. B38 + 1 2 20
  3. C38 + 1 2 19
  4. D39 + 1 2 20

Correct answer

C. 38 + 1 2 19

Step-by-step solution

1 + 3 2 + 7 4 + 15 8 + 31 16 + … = 2 - 1 + 2 - 1 2 + 2 - 1 4 + 2 - 1 8 + 2 - 1 16 + … u p t o   20   t e r m s = 40 - 1 + 1 2 + 1 4 + 1 8 + … u p t o   20   t e r m s = 40 - 1 - 1 2 20 1 - 1 2 = 40 - 2 + 1 2 19 = 38 + 1 2 19

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