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The sum to 10 terms of the series 1 + 2 1.1 + 3 1.1 2 + 4 1.1 3 + . . . . is

Options

  1. A85.12
  2. B92.5
  3. C96.75
  4. D100

Correct answer

D. 100

Step-by-step solution

Let x = 1.1 S = 1 + 2 x + 3 x 2 + . . . . . . . . 10 x 9 and x S = x + 2 x 2 + . . . . . . . . 9 x 9 + 10 x 10 Subtracting, we get, S 1 - x = 1 + x + x 2 + . . . . . . . + x 9 - 10 x 10 = x 10 - 1 x - 1 - 10 x 10 ⇒ - S = x 10 - 1 x - 1 2 - 10 x 10 x - 1 ⇒ - S = 1.1 10 - 1 0.1 2 - 10 1.1 10 0.1 = 100 × 1.1 10 - 100 - 100 × 1.1 10 = - 100 ⇒ S = 100 .

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