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Math Help - Ratio Test of Convergence

  1. #1
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    Ratio Test of Convergence

    I have to decide whether a the summation of a function over [1,infinty) converges or not.
    A particular function is troubling me

    \frac{ln(n)}{n^3}

    I figured the Ratio test would be the best way to go about this. But I got

    \frac{a_{n+1}}{a_{n}} \rightarrow 1

    but seeing as 1 is not <1 or >1, so the test is inconclusive, yes?

    Where would I proceed from here? Does this mean the limit does not exist, hence divergent?
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  2. #2
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    Quote Originally Posted by featherbox View Post
    I have to decide whether a the summation of a function over [1,infinty) converges or not.
    A particular function is troubling me

    \frac{ln(n)}{n^3}
    Use the comparison test.
    You know that \ln(n)<n.
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  3. #3
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    of course! Thanks.
    That's so simple haha.
    Can't believe I missed that.
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