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Let f x = 9 x 9 x + 3 and f x + f 1 - x = 1 then find value of 2 times f 1 1996 + 2 1996 + … . . + f 1995 1996 .

Correct answer

1995

Step-by-step solution

We have, f x = 9 x 9 x + 3 ∴   f x + f 1 - x = 1 ∴   f 1 1996 + f 1 - 1 1996 = 1     . . . i f 2 1996 + f 1 - 2 1996 = 1     . . . i i and so on f 1995 1996 + f 1 - 1995 1996 = 1     . . . i i i Adding all the equation we get, 2   f 1 1996 + f 2 1996 + … + f 1995 1996 = 1995 ⇒   f 1 1996 + f 2 1996 + … + f 1995 1996 = 997 . 5

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