limits - How may I show $x!$ grows faster than $(x+1)^{n-1}$

I am trying to show that the factorial function grows faster than its respective power function.
I started by define $f(x) = \frac {x!} {x^{n}}$ and then looked at $\frac {f(x+1)} {f(x)}$ and got $\frac {x^n} {(x+1)^{(n-1)}}$ and took the limit as n goes to infinity, and got $0$.

If I recall, that's inconclusive, yes?

Note: As I'm typing this, I feel that maybe I should have taken the limit as x goes to infinity, since I am trying to show the argument of $x$ grows.