- #1
mliuzzolino
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Homework Statement
Prove 2n ≤ n! for all n ≥ 4.
Homework Equations
(n+1)! = (n+1)n!
The Attempt at a Solution
First, notice P(4): 24 = 16 = 4*4 ≤ 4*6 = 4 * 3 * 2 * 1 = 4!.
Supposing P(n) is true, check P(n+1):
2n+1 = 2*2n
≤ 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.