# Simplifying a factorial containing only variables

I basically know how Im supposed to do this but I cant think of how to write it out on paper so someone else can follow what I did

I need to find the limit of:

$$\displaystyle\lim_{n \to \infty} \frac{(n/2)!}{n!}$$

I know it will end up approaching zero but I need to show my work, I also know that the top will cancel out to 1 and the bottom will be n(n-1)(n-2)...(n/2 + 1) but I dont know how to show that.

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How is $(n/2)!$ to be interpreted, when $n$ is odd? – Gerry Myerson Feb 11 '13 at 23:16

You can bound it above by something that goes to zero and use the squeeze theorem. You could easily say $\frac {(n/2)!}{n!}\lt \frac 1n$ for example.