Is it even worth the theorem below?
For every positive integer $n$, there is a real number $r$, and $\frac{1}{12n+1} \lt r \lt\frac{1}{12n}$, such that: $$ n! = \sqrt{2n\pi}\left(\frac{n}{e}\right)^n e^r.$$
I saw this statement on some sites, but got no further details. I think the statement refers to an exact value of $n!$, not an approximation.