Q. $\frac{1}{n!} + \frac{1}{2!(n - 2)!} + \frac{1}{4!(n - 4)!} + ...\infty$ is
A) $\frac{2^{n - 1}}{n!}$
B) $\frac{2^{n}}{(n + 1)!}$
C) $\frac{2^{n}}{n!}$
D) $\frac{2^{n - 2}}{(n - 1)!}$
Explanation
(a)
We have, $\frac{1}{n!} + \frac{1}{2!(n - 2)!} + \frac{1}{4!(n - 4)!} + ...\infty$
$\frac{1}{n!}(^{n}C_{o} +^{n}C_{2} +^{n}C_{4} + ...\infty) = \frac{2^{n - 1}}{n!}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.