Can the Binomial Theorem Prove This Series Equals (-2)^n?

[ND3G]

Use binomial theorem to prove

C(n,0) - 3(C(n,1)) + 9(C(n,2) - 27(C(n,3) + ... + (-3)^n(C(n,n) = (-2)^n

From looking at the data given b = (-3) so a = 1 so (-2)^n = (1-3)^n

With this I know the equation in sigma notation and could probably prove the theorem through mathematical induction but I'm not certain that is what they are looking for in this case...

Update:

I proved n=1 and assumed n = k, so do I need to prove n= k+1 through mathematical induction?

 

[Vagrant]

Doesn't writing out the expression for $$(1+x)^n$$ where x=-3 constitute proof?

edit: it's $$(1+x)^n$$