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Let g(x) = ln f(x) where f(x) is a twic...

Let `g(x) = ln f(x)` where f(x) is a twice differentiable positive function on `(0, oo)` such that `f(x+1) = x f(x)`. Then for N = 1,2,3 `g''(N+1/2)- g''(1/2) =`

A

`-4{1+(1)/(9)+(1)/(25)+....+(1)/((2N-1)^(2))}`

B

`4{1+(1)/(9)+(1)/(25)+....+(1)/((2N-1)^(2))}`

C

`-4{1+(1)/(9)+(1)/(25)+....+(1)/((2N-1)^(2))}`

D

`4{1+(1)/(9)+(1)/(25)+....+(1)/((2N-1)^(2))}`

Text Solution

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The correct Answer is:
A
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