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Math Help - prove infinite series?

  1. #1
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    prove infinite series?

    How do I prove this series converges?
    ln x/x^(3/2)
    I think it converges to 0 by using L'Hopital and limits but am not confident in my solving.
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  2. #2
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    Re: prove infinite series?

    Series? Are you summing over x? Is x restricted to the positive integers? Since each term is positive, it certainly cannot sum to 0!

    Or do you mean simply a limit? As x goes to what value? Please post the entire statement of the problem.
    Last edited by HallsofIvy; November 18th 2012 at 05:32 AM.
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  3. #3
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    Re: prove infinite series?

    sigma x=2 to inf
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    Re: prove infinite series?

    Determine if the series converges.
    sigma x=2 to inf, ln(x)/x sqrt x
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    Re: prove infinite series?

    Wolfram says you need to use the Comparison Test, I'm trying to think of a series you could compare it to though...
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    Re: prove infinite series?

    Quote Originally Posted by jnbbieber View Post
    How do I prove this series converges?
    ln x/x^(3/2) I think it converges to 0 by using L'Hopital and limits but am not confident in my solving.
    Assuming this problem is \sum\limits_{k = 2}^\infty  {\frac{{\ln (k)}}{{\sqrt[2]{{k^3 }}}}} .

    Convince yourself that \ln(k)\le 3\sqrt[3]{k}.
    Use the basic comparison with a p-series.
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