# Thread: How do I show that this limit goes to infinity?

1. ## How do I show that this limit goes to infinity?

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".

=infinity

Any input would be greatly appreciated!

2. Originally Posted by s3a
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".

$\lim_{n\rightarrow\infty} \frac{|a_{n+1}|}{|a_{n}|}$