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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

If y = t a n - 1 1 1 + x + x 2 + t a n - 1 1 x 2 + 3 x + 3 + t a n - 1 1 x 2 + 5 x + 7 + . . . . + upto 2 n terms ∀ x ≥ 0 , then y 0 is

Options

  1. At a n - 1 n
  2. Bt a n - 1 2 n
  3. C2 t a n - 1 n
  4. D0

Correct answer

B. t a n - 1 2 n

Step-by-step solution

y = t a n - 1 1 1 + x + x 2 + t a n - 1 1 x 2 + 3 x + 3 + . . . + 2 n terms = t a n - 1 x + 1 - x 1 + x 1 + x + t a n - 1 x + 2 - x + 1 1 + x + 1 x + 2 + . . . . . . 2 n t e r m s = t a n - 1 x + 1 - t a n - 1 x + t a n - 1 x + 2 - t a n - 1 x + 1 + . . . + t a n - 1 x + 2 n - t a n - 1 x + 2 n - 1 = t a n - 1 x + 2 n - t a n - 1 x y 0 = t a n - 1 2 n

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