question_answer

The sum of series\[\frac{1}{2!}+\frac{1}{4!}+\frac{1}{6!}+.....\]is

A) \[\frac{({{e}^{2}}-1)}{2}\]

B)                        \[\frac{{{(e-1)}^{2}}}{2e}\]         

C)        \[\frac{({{e}^{2}}-1)}{2e}\]         

D)        \[\frac{({{e}^{2}}-2)}{e}\]

Correct Answer: B

Solution :

We know that     ?(i) ?.(ii) On adding Eqs. (i) and (ii), we get