You have to prove: e^{C(n,2)} > n!
Okay, now we note that that is equivalent to:
C(n,2) > \textup{ln}(n!)
So if we prove that, we prove what we need to.
We know that:
\textup{ln}(n!) = \textup{ln}(1) + ... + \textup{ln}(n)
We use our inequality, x > \textup{ln}(1+x). So for...