Question

Let $g(x)=\log f(x)$, where $f(x)$ is a twice differentiable positive function on $(0$, $\infty)$ such that $f(x+1)=x f(x)$. Then, for $N=1,2,3, \ldots, g^{\prime \prime}\left(N+\frac{1}{2}\right)-g^{\prime \prime}\left(\frac{1}{2}\right)$ is equal to

Accepted Answer

$-4\left\{1+\frac{1}{9}+\frac{1}{25}+\ldots+\frac{1}{(2 N-1)^2}\right\}$

Answer

$4\left\{1+\frac{1}{9}+\frac{1}{25}+\ldots+\frac{1}{(2 N-1)^2}\right\}$

Answer

$-4\left\{1+\frac{1}{9}+\frac{1}{25}+\ldots+\frac{1}{(2 N+1)^2}\right\}$

Answer

$4\left\{1+\frac{1}{9}+\frac{1}{25}+\ldots+\frac{1}{(2 N+1)^2}\right\}$

JEE MATHEMATICS MCQ: DIFFERENTIATION

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