Question

Prove that : 2ncn = 2^n(1.3.5..........(2n-1)) / n!

Answer 1

Step by step explanation :–

(2n!)

=2

n

(1.3.5...(2n−1))

RHS =(1.3.5...(2n−1))2

n

Multiply and divide by 2.4.6...2n on RHS

[1.3.5...(2n−1)]2

n

=(1.3.5...(2n−1))2

n

×

2.4.6....2n

2.4.6...2n

=

2.4.6....2n

[1.3.5...(2n−1)]2

n

=

2.4.6....2n

[(2n)(2n−1)....5.4.3.2.1]2

n

=

2.4.6....2n

(2n)!2

n

=

2

n

(1.2.3..n)

(2n)!2

n

=

n!

(2n)!

= LHS .proved

I hope it will help you