Question

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

JEE MATHEMATICS MCQ: DIFFERENTIATION

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