Proof the induction 2^n > n+4, n>=3

[arz]

 

[pka]

@arz, can you tell us what steps are require in order to prove a statement is true by induction?
If so then post what you know.

 

[Steven G]

n=3: Is 2^n > n+4? 2^3 =8 and 3+4 =7 so yes!

Now you assume something is true for n=k. What do you assume and what is the restriction on k?

Now you show that something is true for n=k+1. What is it that you want to show?

 

[HallsofIvy]

Assume that, for some k, $\displaystyle 2^k> k+ 4$. Then $\displaystyle 2^{k+1}= 2(2^k)> 2(k+ 4)= 2k+ 8$.
Now you need to show that $\displaystyle 2k+ 8> (k+1)+4= k+ 5$. That looks very easy.