Question

the value of $2^{n}n!\left(\mathrm{1.3.5....}\right(2n-1\left)\right)$ is

• A. $\left(2n\right)!$
• B. $\left(4n\right)!$
• C. $\left(2n\right)!/n$
• D. $n!$

Answer 1

The correct option is A $\left(2n\right)!$

$2^n(n!)(1,3,\mathrm{5.........}(2n-1\left)\right)$

$(2\times 2\times \mathrm{2......}nterms)(1\times 2\times 3.......n)(1,3,5,.....(2n-1)$

$(2\times 4\times 6.......2n)(1,3,5....(2n-1\left)\right)$

$[1,2,3,\mathrm{4...2}n]$

$=\left(2n\right)!$