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Leg g(x)=ln(f(x)), whre f(x) is a twice ...

Leg `g(x)=ln(f(x)),` whre `f(x)` is a twice differentiable positive function on `(0,oo)` such that `f(x+1)=xf(x)dot` 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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