Does the sequence (-0.3)^x converge or diverge?

This is a pretty easy problem I believe, sorry if it's a stupid question. The limit as n approaches infinity is 0, but it is alternating. I have not had a problem that alternates. As long as the limit as n goes to infinity is 0, we have convergence correct?

Also

I then have this Fourier series question

I was given the hint to use the trapezoidal rule for this question.