question_answer

The sum of the series\[1+\frac{1}{4.2!}+\frac{1}{16.4!}+\frac{1}{64.6!}+.....\infty \]is     AIEEE  Solved  Paper-2005

A) \[\frac{e+1}{2\sqrt{e}}\]             

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

C) \[\frac{e+1}{\sqrt{e}}\]                

D)        \[\frac{e-1}{\sqrt{e}}\]

Correct Answer: A

Solution :

We know that, and   putboth sides, we get