Q. The value of $2^{n}\lbrack 1.3.5\ldots(2n - 3)(2n - 1)\rbrack$ is
A) $\frac{(2n)!}{n!}$
B) $\frac{(2n)!}{2^{n}}$
C) $\frac{n!}{(2n)!}$
D) None of these
Explanation
(a)
$\lbrack 1.3.5\ldots\ldots(2n - 1)\rbrack 2^{n}$
$= \frac{1.2.3.4.5.6\ldots..(2n - 1)(2n)2^{n}}{2.4.6\ldots..2n}$
$= \frac{(2n)!2^{n}}{2^{n}(1.2.3\ldots.n)} = \frac{(2n)!}{n!}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.