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JEE Main20231 Feb 2023Morning ShiftMathematicsSequences and SeriesActual

The sum to 10 terms of the series 1 1 + 1 2 + 1 4 + 2 1 + 2 2 + 2 4 + 3 1 + 3 2 + 3 4 + … is :-

Options

  1. A59 111
  2. B55 111
  3. C56 111
  4. D58 111

Correct answer

B. 55 111

Step-by-step solution

We have, 1 1 + 1 2 + 1 4 + 2 1 + 2 2 + 2 4 + 3 1 + 3 2 + 3 4 + … Here, t n = n 1 + n 2 + n 4 = n ( n 2 + n + 1 ) ( n 2 - n + 1 ) So, t 1 = 1 2 1 - 1 3 t 2 = 1 2 1 3 - 1 7         ⋮         ⋮         ⋮         ⋮         ⋮         ⋮         ⋮         ⋮         ⋮ t 10 = 1 2 1 91 - 1

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