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Math Help - Infinite Series convergence or divergence

  1. #1
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    Infinite Series convergence or divergence

    Please explain how to determine for the following infinite series using comparison test.

    n=1, 1/n(n+2)(n+3)
    We compare to 1/n^3 ??? Is it harmonic series??? p=3, is greater than 1. It means that the series converges.

    Please solve this. Thank you very much
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  2. #2
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    Quote Originally Posted by oceanmd View Post
    Please explain how to determine for the following infinite series using comparison test.

    n=1, 1/n(n+2)(n+3)
    We compare to 1/n^3 ??? Is it harmonic series??? p=3, is greater than 1. It means that the series converges.

    Please solve this. Thank you very much
    Solve what? You just gave the answer. No, it not, strictly speaking a "harmonic series"- that is specifically 1+ 1/2+ 1/3+ 1/4+...

    But you are correct that this series converges since n+2> n and n+3> n
    1/(n(n+2)(n+3))< 1/n^3 and, by the "p-text" you cite, 1/n^3 converges so 1/(n(n+2)(n+3)) converges by the "comparison test".
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