So you know how $1+2+3+...+n= \frac{n(n+1)}{2}$, wouldn't it be nice if $1 \cdot 2 \cdot 3 \cdot ... \cdot n = \sqrt{n^{n}}$.
Well, turns out it's an okay approximation for small values of n, the general form would be $\sqrt{n^{kn}}$ where k approaches 2 as n goes to infinity. I might play around with this for a little while to see if I can know how to express k in terms of recursive approximations.