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Let g(x)=log(e)f(x) where f(x) is twice ...

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

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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