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Math Help - Convergence of series

  1. #1
    Ant
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    Convergence of series

    Hi,

    \sum_{n=1}^\infty \frac{n+2}{n^3 +1}

    I tried using the ratio test (ended up with 1 so wasn't helpful), similarly the nth root test and integral comparison test didn't work.

    Can I say that:

    frac{n+2}{n^3 +1} \leq \frac{1}{n^2}" alt="\frac{n+2}{n^3 +1} \leq \frac{1}{n^2}" />

    and 1/n^2 converges by the integral comparison test, so by the comparison theorem, the sum converges?

    Is the above correct? Thanks

    edit: I couldn't get the Latex to work so I've taken off the tags, sorry!

    Last edited by Ant; May 23rd 2012 at 03:38 PM.
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  2. #2
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    Re: Convergence of series

    try the limit comparison test with the known convergent series \sum \frac{1}{n^2}
    Thanks from Ant
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  3. #3
    Member anonimnystefy's Avatar
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    Re: Convergence of series

    Hi

    To use LaTeX put (TEX)(/TEX) tags around the text you want texified except that you shoul put [ instead of ( and ] instead of ) .
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  4. #4
    Ant
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    Re: Convergence of series

    Thanks for the help. That's what I did, I just wasn't sure if it was right. Thank you!

    When I put the tags around it comes up like this \sum_{n=1}^\infty \frac{n+2}{n^3 +1}

    edit: it's working now! but I literally just copied and pasted form my original post! I'll try again.
    Last edited by Ant; May 23rd 2012 at 03:39 PM.
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  5. #5
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    Re: Convergence of series

    Quote Originally Posted by Ant View Post
    Thanks for the help. That's what I did, I just wasn't sure if it was right. Thank you!

    When I put the tags around it comes up like this \sum_{n=1}^\infty \frac{n+2}{n^3 +1}

    edit: it's working now! but I literally just copied and pasted form my original post! I'll try again.
    Simple comparison works.
    \sum_{n=1}^\infty \frac{n+2}{n^3 +1}\le \sum_{n=1}^\infty \frac{2}{n^2 }
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