Question

Let g (x) = log f (x) where f (x) is twice differentible positive function on (0, ∞) such that f (x + 1) = x f (x). Then, for N = 1, 2, 3, ...........
$g''\bigg \lgroup N + \frac{1}{2}\bigg \rgroup - g''\bigg \lgroup \frac{1}{2}\bigg \rgroup =$
$(a) -4\bigg \{1+\frac{1}{9}+\frac{1}{25}+......+\frac{1}{(2N-1)^2}\bigg \}\\(b) 4\bigg \{1+\frac{1}{9}+\frac{1}{25}+......+\frac{1}{(2N-1)^2}\bigg \}\\(c) -4\bigg \{1+\frac{1}{9}+\frac{1}{25}+......+\frac{1}{(2N+1)^2}\bigg \}\\(d) 4\bigg \{1+\frac{1}{9}+\frac{1}{25}+......+\frac{1}{(2N+1)^2}\bigg \}$

Answer 1

Answer:c

Step-by-step explanation: