if you need to prove 3^n>c*2^n for any natural number you could always go by the easiest(infact its most effective as well in many cases) way that is proof by induction.the steps you need are:

1)first prove it for 1 assuming it to be true for n.

2)then prove it for 2 .

3)Now prove it for n+1.

4)while proving for n+1, substitute values you got for n which was assumed to be true earlier.

5)if this results into the relation being true for n+1 then you are done.

speaking frankly i never understood how this is a proof. perhaps it shows that since for every n and n+1 the relation is true therefore it is true for all natural numbers. natural numbers progress uniformly. so perhaps like that!