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Math Help - Are these series convergent?

  1. #1
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    Are these series convergent?

    Hi there,

    I need a little help with testing the following series for convergence:

    \sum_{n = 1}^\infty (7 - 4n + 5n^3)/(2n^3 - 6n + 3)

    I'm sure this is very basic and doesn't involve using the limit comparison test or the ratio test but although i know it's a convergent sequence, it's just not obvious to me how to solve it. I'd appreciate any help pointing me in the right direction.

    Thanks.
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  2. #2
    Super Member girdav's Avatar
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    Compute the limit of the term you have to sum.
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  3. #3
    MHF Contributor
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    A necessary condition for a series to be convergent is that \displaystyle \lim_{n \to \infty}a_n = 0.

    So a basic test for divergence is to evaluate \displaystyle \lim_{n \to \infty}a_n and show that it \displaystyle \neq 0.
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  4. #4
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    Yes, I get it now! Thanks for the help guys.
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