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Math Help - convergence question..

  1. #1
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    convergence question..

    \sum_{1}^{\infty}\frac {2^k+k^3}{\sqrt k 3^k}

    how to show if it converges or not?
    Last edited by transgalactic; July 12th 2011 at 02:05 AM.
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  2. #2
    Super Member girdav's Avatar
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    Re: convergence question..

    Ratio test should work here.
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  3. #3
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    Re: convergence question..

    Have you tried the ratio test?
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  4. #4
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    Re: convergence question..

    sorry i havd a typo ,its
    \sum_{1}^{\infty}\frac {2^k+k^3}{\sqrt k 3^k}
    i tried this law.
    i got limit k goes to infinity of
    2(\frac{k+1}{k})^3 \frac{\sqrt{k}+3^k}{\sqrt{k+1}+3^{k+1}}
    is it ok to solve each fracture as if there where to different limits
    and then multiply the results?
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  5. #5
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    Re: convergence question..

    I'm not sure what you've done.

    You need to evaluate \displaystyle \lim_{k \to \infty}\left|\frac{a_{k+1}}{a_k}\right|, which in this case is

    \displaystyle \lim_{k \to \infty}\left|\frac{\frac{2^{k+1}+(k+1)^3}{3^{k+1} \sqrt{k+1}}}{\frac{2^k+k^3}{3^k\sqrt{k}}}\right|
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  6. #6
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    Re: convergence question..

    thats was done but we get a multiplication
    of two differenent fractures
    which could be solve apart only
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