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Let g(x) = log f(x), where f(x) is a twi...

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

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

Verified by Experts

The correct Answer is:
a
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