(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove the Inequality for the indicated integer values of n.

[tex]n!>2^n,n\geq4[/tex]

2. Relevant equations

3. The attempt at a solution

For n=4 the formula is true because

[tex]4!>2^4[/tex]

Assume the n=k

[tex]k!>2^k[/tex]

Now I need to prove the equation for k+1

I can multiply both sides by 2 and have

[tex]2(k!)=2(k!)>(2)2^k=2^{k+1}[/tex]

Is this what you would do next? I'm not quite sure what to do past this point.

[tex]2(k!)>2^{k+1}>k+1[/tex]

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# Homework Help: Inequality Mathematical Induction

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