In the limit:

lim as n--->inf 2*(n!)/4^n = 2*lim as n--->inf (n!)/4^n

how do I show that n! grows faster than 4^n?

This is not a proof question. It's just a "do it" question and I'm asking for the "how".

The answer:

=infinity

Any input would be greatly appreciated!

Thanks in advance!