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The sum of first 9 terms of the series 1 3 1 + 1 3 + 2 3 1 + 3 + 1 3 + 2 3 + 3 3 1 + 3 + 5 + . . . is

Options

  1. A192
  2. B71
  3. C96
  4. D142

Correct answer

C. 96

Step-by-step solution

Given, 1 3 1 + 1 3 + 2 3 1 + 3 + 1 3 + 2 3 + 3 3 1 + 3 + 5 + . . . ∴   T n = 1 3 + 2 3 + ... + n 3 1 + 3 + ... + 2 n - 1 = n 2 n + 1 2 4 n 2 = n + 1 2 4 Sum of 9 terms = ∑ n = 1 9 n + 1 2 4 = 1 4 2 2 + 3 2 + . . . + 1 0 2 = 1 4 1 2 + 2 2 + . . . + 1 0 2 - 1 2 = 1 4 1 0 · 1 1 · 2 1 6 - 1 = 1 4 3 8 4 = 9 6

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