help with proof

4chan, i require your assistance:
prove that 2^n+(-1)^(n+1) for n>=2 is always divisible by 3.

Any pointers on where to start? I know your not going to do my homework for me, this isn't actually the homework question, but if i can prove this then it proves what im trying to prove. Just some tips maybe ? thanks.

2 is congruent to -1 modulo 3, so 2^n is congruent to (-1)^n modulo 3. (-1)^n + (-1)^(n+1) = (-1)^n(1 + -1) = 0, so 2^n + (-1)^(n+1) is congruent to 0 modulo 3.