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Math Help - How do I show that this sum converges?

  1. #1
    s3a
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    How do I show that this sum converges?

    I'm trying to use the integral test but I have a little problem. I don't know if I am allowed to use l'hopital's rule in integrals because having ln(n)/n^3 would give me 1/3n^3 after applying l'hopital's rule and I can show that 1/n^3 is convergent using the integral test and the comparison test as well however I have a feeling that I am not allowed to use l'hopital's rule in this case, so...what do I do?

    Any input would be greatly appreciated!
    Thanks in advance!
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  2. #2
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    Quote Originally Posted by s3a View Post
    I'm trying to use the integral test but I have a little problem. I don't know if I am allowed to use l'hopital's rule in integrals because having ln(n)/n^3 would give me 1/3n^3 after applying l'hopital's rule and I can show that 1/n^3 is convergent using the integral test and the comparison test as well however I have a feeling that I am not allowed to use l'hopital's rule in this case, so...what do I do?

    Any input would be greatly appreciated!
    Thanks in advance!
    That series is a p-series. You should what you know about p series to solve this series.
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  3. #3
    s3a
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    If by that you mean knowing that the sum from 1 to inf of 1/n^3 is convergent then I know that but how does that help me given that 1/n^3 < ln(n)/n^3 ?
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  4. #4
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    What is the original problem conditions?

    \frac{1}{n^3}

    This?
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  5. #5
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    you should know that n>ln(n)

    so

    \frac{ln(n)}{n^3} \leq \frac{n}{n^3} = \frac{1}{n^2}

    so ...?
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