Hi there folks, I have just a small problem with a specific induction problem. The problem itself is: "Prove [tex]n! > 4^n[/tex], for all n >= 9."(adsbygoogle = window.adsbygoogle || []).push({});

So here's my work:

1) Show true for n = 9

LS

9! = 362880

RS

4^9 = 262144

.:. LS > RS

2) Assume true for n = k

i.e. Assume that k! > 4^k

3) Prove true for n = k+1

i.e. Prove that (k+1)! > 4^(k+1)

So I begin to expand the LHS out

(k+1)! = (k+1)(k)!

> (K+1)(4^k) (by induction hypothesis)

this is the problem that I encounter. I get stuck here because I don't exactly know how to followthrough at this point. How does (k+1)(4^k) become greater that 4^(k+1) ?

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# Mathematical Induction trouble with 1 step!

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