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Sum of the series P = 1 2 1 + 2 + 1 3 2 + 2 3 + 1 4 3 + 3 4 + … + 1 100 99 + 99 100 is

Options

  1. A1 10
  2. B3 10
  3. C9 10
  4. D1 2

Correct answer

C. 9 10

Step-by-step solution

t r = 1 r + 1 r + r r + 1 = 1 r r + 1 r + 1 + r × r + 1 - r r + 1 - r = r + 1 - r r r + 1 = 1 r - 1 r + 1 P = ∑ r = 1 99 t r = 1 - 1 100 = 9 10

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