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Math Help - Another series problem

  1. #1
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    Another series problem

    Hi,

    I want to see if this series is convergent but I'm a bit lost.

    \sum_{n = 1}^\infty (5 - 2cos n)/(3n^3 + n + 2).

    Obviously it's dominated by 1/n^3, and i'm sure it is convergent, but I'm struggling to manipulate the expression to prove this. Any advice on how to get going?

    Thanks.
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  2. #2
    Super Member girdav's Avatar
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    Since |5-2\cos n|\leq 5+2=7 and 3n^3+n+2\geq 3n^3, we get \left|\frac{5-2\cos n}{3n^3+n+2}\right|\leq \frac 7{3n^3}.
    It's not dominated by \frac 1{n^3} but by something with the form \frac C{n^3}.
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  3. #3
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    I would never have thought of solving it that way but it makes sense. Thanks for your help Girdav.
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