Math Help - Converging/Diverging Sequence

1. Converging/Diverging Sequence

Prove whether the following sequence converges or diverges.

$\{\frac{n!}{2^n} \}\limits^\infty_{n=0}$

Since it is a sequence I cannot use any of the tests used for series. Any help would be appreciated.

2. If $n\ge 4$ then $n!>2^n$.
What should that tell you?

3. Originally Posted by Plato
If $n\ge 4$ then $n!>2^n$.
What should that tell you?
Yeah I know the sequence goes to infinity and that factorials grow much faster than exponentials but is there some other way to prove it? Like taking a limit or is this the only way?

4. The fact that f(n) > g(n) does not determine whether $\lim_{n\to\infty}f(n)/g(n)$ exists. However, it is easy to show that $\frac{1}{2}\cdot\frac{2}{2}\cdot\ldots\cdot \frac{n}{2}$ becomes arbitrarily large.

I know the sequence goes to infinity
This is a synonym for "diverges".