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JEE Main202125 Feb 2021Evening ShiftMathematicsFunctionsActual

A function f ( x ) is given by f x = 5 x 5 x + 5 , then the sum of the series f 1 20 + f 2 20 + f 3 20 + … + f 39 20 is equal to:

Options

  1. A19 2
  2. B49 2
  3. C39 2
  4. D29 2

Correct answer

C. 39 2

Step-by-step solution

f x = 5 x 5 x + 5    and   f 2 - x = 5 5 x + 5 f x + f 2 - x = 1 ⇒ f 1 20 + f 2 20 + … + f 39 20 = f 1 20 + f 39 20 + … + f 19 20 + f 21 20 + f 20 20 = 19 + 1 2 = 39 2

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