MCQ
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 $\mathrm{N}=1,2,3, \ldots$,
$\mathrm{g}^{\prime \prime}\left(\mathrm{N}+\frac{1}{2}\right)-\mathrm{g}^{\prime \prime}\left(\frac{1}{2}\right)=$
- ✓$-4\left\{1+\frac{1}{9}+\frac{1}{25}+\ldots+\frac{1}{(2 \mathrm{~N}-1)^2}\right\}$
- B$4\left\{1+\frac{1}{9}+\frac{1}{25}+\ldots+\frac{1}{(2 \mathrm{~N}-1)^2}\right\}$
- C$-4\left\{1+\frac{1}{9}+\frac{1}{25}+\ldots+\frac{1}{(2 \mathrm{~N}+1)^2}\right\}$
- D$4\left\{1+\frac{1}{9}+\frac{1}{25}+\ldots+\frac{1}{(2 \mathrm{~N}+1)^2}\right\}$