Question

Let $g(x)=\log _e f(x)$, where $f(x)$ is twice differentiable positive function on $(0, \infty)$ such that $f(x+1)=x f(x)$, for $N=1,2,3, \ldots$, then $g''\left( {N + \frac{1}{2}} \right) - g''\left( {\frac{1}{2}} \right){\rm{ equals }}$

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

More Questions from DIFFERENTIATION