Possible Duplicate:
Prove that $\frac{n^n}{3^n} < n! < \frac{n^n}{2^n} $ for each $ n \geq 6 $
I want to prove $\dfrac{n^n}{3^n} \lt n! \lt \dfrac{n^n}{2^n}$ for all $n$ $\geq$ 6:
So we do the base case with $n$ = $6$ and it is really exciting.
Now for the induction hypothesis we assume the formula to be true. I started out by doing simple manipulations with $n+1$, however I get nowhere... (well I actually got close but my iff was actually just an if then...)
- How can I get this off of the ground?
- What pieces of information can I use?
- Thanks!