Mathematical Induction Check, $n! \leq n^n/2^n $ Hello I am working on this problem and was wondering if I did the proof correct.
Use induction to prove that $n! \leq n^n/2^n $ for all $n \geq 6$.
Basic Step (n=6): 6! $\leq 6^6/2^3 = 3^6$
Thus $80 \leq 81$, so the Basic Step is true.
Assume the statement above is true for n. We need to show n+1 is also true.
$(n+1)^{n+1}/2^{n+1} = (n+1)^n (n+1)/2^{n+1} \geq n^n(n+1)/2^{n+1} \geq n^n/2^{n+1} \geq n^n/2^n \geq n!$

Hint: You're very close, but not quite there. Remember that $(n+1)!=(n+1)n!$.
