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JEE Main202126 Feb 2021Morning ShiftMathematicsSequences and SeriesActual

The sum of the infinite series 1 + 2 3 + 7 3 2 + 12 3 3 + 17 3 4 + 22 3 5 + … … is equal to:

Options

  1. A9 4
  2. B15 4
  3. C11 4
  4. D13 4

Correct answer

D. 13 4

Step-by-step solution

S = 1 + 2 3 + 7 3 2 + 12 3 3 + 17 3 4 + … S 3 = 1 3 + 2 3 2 + 7 3 3 + 12 3 4 + … 2 S 3 = 1 + 1 3 + 5 3 2 + 5 3 3 + 5 3 4 + … + up to infinite terms ⇒ 2 S 3 = 4 3 + 5 9 1 1 - 1 3 ⇒ 2 S 3 = 13 6 ⇒ S = 13 4

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