Question

The value of $1\times 3\times 5....\times (2n-1)$ $\times 2^n=$

• A. $\frac{\left(2n\right)!}{2^n}$
• B. $\frac{\left(2n\right)!}{n!}$
• C. $\frac{n!}{\left(2n\right)!}$
• D. $2n$

Answer 1

The correct option is B $\frac{\left(2n\right)!}{n!}$

$x=1\times 3\times 5\times \mathrm{7.......}(2n-1)\times 2^{n}x=\frac{1\times 2\times 3\times \mathrm{4.........}(2n-1)\times 2n\times 2^n}{2\times 4\times 6\times \mathrm{8.....2}n}x=\frac{\left(2n\right)!\times 2^n}{2^n\times (1\times 2\times 3\times ........n)}x=\frac{\left(2n\right)!\times 2^n}{2^n\times n!}x=\frac{\left(2n\right)!}{n!}$