# Simplifying a Factorial

1. Jan 25, 2014

### vanceEE

1. The problem statement, all variables and given/known data

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

How do you simplify this factorial?

2. Jan 25, 2014

### vanhees71

Just write out the factorials. Then you'll see immediately how to simplify the expression.

3. Jan 25, 2014

### vanceEE

I cannot tell from writing them out.
$$\frac{1*3*5*7*9...(2n-1)!}{3*5*7*9*11...(2n+1)!}$$

Edit:
Nvm, I understand. Thank you!

$$\frac{(2n-1)!}{(2n+1)!} = \frac{(2n-1)*(2n-2)*(2n-3)*(2n-4)...2*1}{(2n+1)*(2n)*(2n-1)*(2n-2)...2*1}$$
$$= \frac{1}{(2n)*(2n+1)}$$

or

$$\frac{(2n-1)!}{(2n+1)!} = \frac{(2n-1)!}{(2n+1)*(2n)*(2n-1)!}$$
$$= \frac{1}{(2n+1)*(2n)}$$

Last edited: Jan 25, 2014