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Proof the inequality $n! \geq 2^n$ by induction
Prove By Induction that $n!>2^n$

I have to prove the inequality $n! > 2^n$ for all integers $n \geq4$.

I am having trouble with this.

I am assuming that: $n! > 2^n \implies (n+1)! > 2^{n+1}$.

I have proven the base case is true, as $4! > 2^4$.

For the induction step, I get: $(n+1)! = (n+1)n!$

After that, I am not sure what to do.



marked as duplicate by Ilya, Sasha, David Mitra, davidlowryduda, user940 Feb 20 '12 at 19:39

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