I'm trying to use induction to prove this. I'm sure it's a simple proof, but I can't seem to get over the first few steps. Any help?
$P(7) = 3^7<7! \rightarrow$ True.
Assume $P(k) = 3^k<k!$
Now we must prove $P(k+1)$. Here's where I'm lost. If I'm adding a +1 to the exponent on the LHS, where would I add it to the factorial on the RHS?