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JEE Main202225 Jul 2022Evening ShiftMathematicsSequences and SeriesActual

The sum ∑ n = 1 21 3 4 n - 1 4 n + 3 is equal to

Options

  1. A7 87
  2. B7 29
  3. C14 87
  4. D21 29

Correct answer

B. 7 29

Step-by-step solution

∑ n = 1 21 3 4 n - 1 4 n + 3 = 3 4 ∑ n = 1 21 1 4 n - 1 - 1 4 n + 3 = 3 4 1 3 - 1 7 + 1 7 - 1 11 + … . + 1 83 - 1 87 = 3 4 1 3 - 1 87 = 3 4 84 261 = 7 29

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