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Math Help - Sequence Convergence (easy) and fourier series question

  1. #1
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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

    Sequence Convergence (easy) and fourier series question-screen-shot-2012-04-09-7.11.30-pm.png

    I was given the hint to use the trapezoidal rule for this question.
    Last edited by as1592; April 9th 2012 at 05:18 PM.
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  2. #2
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    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.
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