Determin if its Convergent or Divergent

[thatguy47]

I need to determine whether the series converges or diverges and solve it. Its a geometric series:

I think it diverges but I'm not sure how to solve it/know for sure if it diverges.

 

[royhaas]

Note that \(\displaystyle sin(n\pi)=0\) if \(\displaystyle n\) is an integer.