1. ## Proof question

My question Prove that $3^n > n!$ whenever n is a positive integer greater than 6

Can you help me please ı can't solve this proof

2. Originally Posted by jacklarson
My question Prove that $3^n > n!$ whenever n is a positive integer greater than 6

Can you help me please ı can't solve this proof
Try using induction.

Base step: $n = 7$

$3^7 = 2187$

$7! = 5040$

The statement is clearly not true...

3. Originally Posted by jacklarson
My question Prove that $3^n > n!$ whenever n is a positive integer greater than 6

Can you help me please ı can't solve this proof
It's $3^n. Try induction or any of the other twenty applicable methods.

4. Originally Posted by Drexel28
It's $3^n. Try induction or any of the other twenty applicable methods.
Just curious, what are the other methods?
Do you mind listing them?

5. Originally Posted by novice
Just curious, what are the other methods?
Do you mind listing them?
Note that $\frac{3^n}{n!}=\frac{3}{n}\cdots\frac{3}{n}$ and show that this is less than one. Prove that there is an injection from the set of all permutations of $\left\{1,\cdots,n\right\}$ to the set of all true ordering relations on $\left\{1,\cdots,n\right\}$. etc.