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JEE Main20199 Apr 2019Evening ShiftMathematicsSequences and SeriesActual

The sum of the series 1 + 2 × 3 + 3 × 5 + 4 × 7 + … upto 11 t h term is:

Options

  1. A945
  2. B916
  3. C946
  4. D915

Correct answer

C. 946

Step-by-step solution

Given series is 1 + 2 × 3 + 3 × 5 + 4 × 7 + 5 × 9 + … Thus, the general term is T r = r 2 r - 1 Hence, the sum of 11 terms of the series is S 11 = ∑ r = 1 11 r 2 r - 1 ⇒ S 11 = 2 ∑ r 2 - ∑ r Using the formulae for ∑ r 2 r = 1 n = n n + 1 2 n + 1 6 and ∑ r r = 1 n = n n + 1 2 , we get S 11 = 2 ⋅ 11 11 + 1 22 + 1 6 - 11 11 + 1 2 ⇒ S 11 = 44 × 23 - 66 ⇒ S 11 = 1012 - 66 = 946 .

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