Question

The value of $2^n[\mathrm{1.3.5...}(2n-3)(2n-1)]$ is

• A. $\frac{\left(2n\right)!}{n!}$
• B. $\frac{\left(2n\right)!}{2^n}$
• C. $\frac{n!}{\left(2n\right)!}$
• D. None of these

Answer 1

Answer: (A)

$[\mathrm{1.3.5......}(2n-1)]2^n$
$=\frac{\mathrm{1.2.3.4.5.6....}\left(2n-1\right)\left(2n\right)2^n}{\mathrm{2.4.6......2}n}=\frac{\left(2n\right)!2^n}{2^n\left(\mathrm{1.2.3...}n\right)}=\frac{\left(2n\right)}{n!}$