I need to know if the factorial function is decreasing.

This is the second condition for the Alternating Series Test.

The Alternating Series:

$\displaystyle

\Sigma^{\infty}_{k = 1} (-1)^{k-1}\frac{k!}{(2k-1)!}

$

I need to show that

$\displaystyle

f(x) = \frac{x!}{(2x-1)!}

$

decreasing.

Normally, I just take the first derivative but since I have a factorial I don't know.

Can someone let me know how I have to do that?

Thanks.