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The sum to n terms of the series 1 2 + 3 4 + 7 8 + 15 16 + is

Options

  1. An-1-2^ -n
  2. B1
  3. Cn-1+2^ -n
  4. D1+2^ -n

Correct answer

C. n-1+2^ -n

Step-by-step solution

aligned 1 2 + 3 4 + 7 8 + 15 16 + =& (1- 1 2 )+ (1- 1 4 )+ (1- 1 8 )+ (1- 1 16 )+ . =& n - 1 2 1- 1 2^ n 1- 1 2 = n -1+2^ - n aligned

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