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JEE Main20205 Sep 2020Morning ShiftMathematicsInverse Trigonometric FunctionsActual

If S is the sum of the first 10 terms of the series, tan - 1 1 3 + tan - 1 1 7 + tan - 1 1 13 + tan - 1 1 21 + … … then tan ( S ) is equal to :

Options

  1. A5 6
  2. B5 11
  3. C- 5 6
  4. D10 11

Correct answer

A. 5 6

Step-by-step solution

S = tan - 1 1 3 + tan - 1 1 7 + tan - 1 1 13 + … … up to 10 terms. S = tan - 1 2 - 1 1 + 1 . 2 + tan - 1 3 - 2 1 + 2 . 3 + tan - 1 4 - 3 1 + 3 . 4 + … … + tan - 1 11 - 10 1 + 11 . 10 ⇒ S = tan - 1 2 - tan - 1 1 + tan - 1 3 - tan - 1 2 + … … + tan - 1 11 - tan - 1 10 ⇒ S = tan - 1 11 - tan - 1 1 ⇒ S = tan - 1 11 - 1 1 + 11 · 1 = tan - 1 10 12 ∴ tan ( S ) = 5 6

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