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Sequence Convergence (easy) and fourier series question

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

Attachment 23551

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

Re: Sequence Convergence (easy) and fourier series question

I don't know anything about Fourier series yet so I can't answer that question, but I can tell you that your sequence converges. For a sequence, if the limit as n approaches infinity exists as a real number than the sequence converges. Zero is a real number so your sequence does converge.