Wednesday, December 9, 2015

calculus - Show that $ lim_{n rightarrow infty} frac{n!}{2^{n}} = infty $

Show that $ \lim_{n \rightarrow \infty} \frac{n!}{2^{n}} = \infty $




I know what happens intuitively....



$n!$ grows a lot faster than $2^{n}$ which implies that the limit goes to infinity, but that's not the focus here.



I'm asked to show this algebraically and use the definition for a limit of a sequence.



"Given an $\epsilon>0$ , how large must $n$ be in order for $\frac{n!}{2^{n}}$ to be greater than this $\epsilon$ ?"



My teacher recommends using an inequality to prove it but I'm feeling completely lost...

No comments:

Post a Comment

analysis - Injection, making bijection

I have injection $f \colon A \rightarrow B$ and I want to get bijection. Can I just resting codomain to $f(A)$? I know that every function i...