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JEE Advanced2013MathematicsSequences and SeriesActual

Let S n = Σ k = 1 4 n - 1 k k + 1 2 k 2 . Then S n can take value(s)

Options

  1. A1056
  2. B1088
  3. C1120
  4. D1332

Correct answer

A. 1056

Step-by-step solution

Given S n = Σ k = 1 4 n - 1 k k + 1 2 k 2 = - 1 2 - 2 2 + 3 2 + 4 2 - 5 2 - 6 2 + 7 2 + 8 2 + ............ = 3 2 - 1 + 4 2 - 2 2 + 7 2 - 5 2 + 8 2 - 6 2 ............ = 2 1 + 3 + 2 + 4 + . . . + 4 n = 2 4 n 4 n + 1 2 = 4 n 4 n + 1 S n = 1056 is true for n = 8 S n = 1332 is true for n = 9

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