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## Homework Statement

Prove 2

^{n}≤ n! for all n ≥ 4.

## Homework Equations

(n+1)! = (n+1)n!

## The Attempt at a Solution

First, notice P(4): 2

^{4}= 16 = 4*4 ≤ 4*6 = 4 * 3 * 2 * 1 = 4!.

Supposing P(n) is true, check P(n+1):

2

^{n+1}= 2*2

^{n}

**≤ 2 * n!**

≤ (n+1)*n!

= (n+1)!

Q.E.D.

I know I'm going wrong in the bold red step as I'm using the very statement I'm trying to prove. I have no idea what to do at this step.