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Math Help - Finding the Interval and Radius of Convergence

  1. #1
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    Finding the Interval and Radius of Convergence

    The equation is: Summation n=1 to inf x^n/(n+1)

    When the endpoints are checked at x=1 - 1^n/(n+1) is rewritten as 1/n - 1. Can somebody show me the validity of this?

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  2. #2
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    It really doesn't matter because  \sum_{n=0}^{\infty} \frac{1}{n+1} behaves like  \sum_{n=0}^{\infty} \frac{1}{n} by the limit camparison test.
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  3. #3
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    That's true. But I would still like to know.
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  4. #4
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    I don't think it can be \sum_{n=0}^{\infty} \frac{1}{n} -1 because if you make it into an improper fraction, you get \sum_{n=0}^{\infty} \frac{1-n}{n} which diverges.
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  5. #5
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    Hi p75213...are you a Stargate fan? (if you get that, you are )

    Anyway, your problem is in the form of the ratio test for convergence, which basically lets you compare your series to a geometric series to determine it's behavior. I think you'll find your proof here.

    http://www.math.scar.utoronto.ca/cal...ture43-rev.pdf

    Hope that helps,
    Be well,
    T
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