The value of 2 n { 1.3.5..... ( 2 n − 3 ) ( 2 n − 1 ) } is Options: A . &nbsp ( 2 n ) ! n ! B . &nbsp ( 2 n ) ! 2 n C . &nbsp n ! ( 2 n ) ! D . &nbsp ( 2 n − 1 ) ! n !

Answer: Option A : A 1.3.5...... ( 2 n − 1 ) 2 n = 1.2.3.4.5.6.... ( 2 n − 1 ) ( 2 n ) 2 n 2.4.5.....2 n = ( 2 n ) ! 2 n 2 n ( 1.2.3...... n ) = ( 2 n ) ! n !

The value of 2n{1.3.5.....(2n−3)(2n−1)} is

Question

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

Options:

A .

\frac{(2 n)!}{n!}

B .

\frac{(2 n)!}{2^{n}}

C .

\frac{n!}{(2 n)!}

D .

\frac{(2 n - 1)!}{n!}

Answer: Option A
:
A

$1.3.5...... (2 n - 1) 2^{n}$ = $\frac{1.2.3.4.5.6.... (2 n - 1) (2 n) 2^{n}}{2.4.5.....2 n}$

= $\frac{(2 n)! 2^{n}}{2^{n} (1.2.3...... n)}$ = $\frac{(2 n)!}{n!}$

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