The sum of the series <br> $1 + \frac{1}{4.2!} + \frac{1}{16.4!} + \frac{1}{64.6!}. . . . \infty$ is :

Question

( A ) $\frac{e+1}{2\sqrt{e}}$
( B ) $\frac{e-1}{\sqrt{e}}$
( C ) $\frac{e+1}{\sqrt{e}}$
( D ) $\frac{e-1}{2\sqrt{e}}$