- #1
themadhatter1
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Homework Statement
Prove the Inequality for the indicated integer values of n.
[tex]n!>2^n,n\geq4[/tex]
Homework Equations
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]