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The sum of the series 1 2 3 2 + 2 1 3 2 + 3 2 + 3 2 3 2 + . . . . . . to 10 terms is

Options

  1. A1390 9
  2. B1790 9
  3. C1990 9
  4. D2290 9

Correct answer

D. 2290 9

Step-by-step solution

1 2 3 2 + 2 1 3 2 + 3 2 + 3 2 3 2 + . . . . . . . . to 10 terms = 5 3 2 + 7 3 2 + 9 3 2 + 11 3 2 . . . . . . . . to 10 terms = 5 2 + 7 2 + 9 2 + 1 1 2 + . . . . . 9 to 10 terms = 1 9 ∑ r = 1 10 2 r + 3 2 = 1 9 4 ∑ r = 1 10 r 2 + 12 ∑ r = 1 10 r + 9 ∑ r = 1 10 1 = 1 9 2 4 × 10 × 11 × 21 7 6 3 + 6 12 × 10 × 11 2 + 9 × 10 = 1 9 1540 + 660 + 90 = 2290 9

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