Prove whether the following sequence converges or diverges.
$\displaystyle \{\frac{n!}{2^n} \}\limits^\infty_{n=0}$
Since it is a sequence I cannot use any of the tests used for series. Any help would be appreciated.
The fact that f(n) > g(n) does not determine whether $\displaystyle \lim_{n\to\infty}f(n)/g(n)$ exists. However, it is easy to show that $\displaystyle \frac{1}{2}\cdot\frac{2}{2}\cdot\ldots\cdot \frac{n}{2}$ becomes arbitrarily large.
This is a synonym for "diverges".I know the sequence goes to infinity