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Math Help - Convergence

  1. #1
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    Convergence

    Use the appropriate test to decide whether the following series converge or not:

    a) \sum \limit_{n=1} ^{\infty} \frac{3n^2 - 2n + 1}{2n^2 + 5}

    b) \sum \limit_{n=1} ^{\infty} \frac{3n^2 - 2n + 1}{2n^4 + 5}

    c) \sum \limit_{n=1} ^{\infty} \frac{n^3 4^n}{3(n!)}

    d) \sum \limit_{n=1} ^{\infty} \frac{2 + 3 sin~n}{5n^2 + 2}

    Could someone please help :-). Thank you
    Last edited by Natasha1; May 23rd 2006 at 09:35 AM.
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  2. #2
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    a) A series does not converge if the terms do not tend to zero. In this series the terms tend to 3/2.

    b) A series converges if the absolute value of each term is less than the corresponding term of a series known to converge. In this case compare with the series 2/n^2.

    c) A series converges if the ratio of successive terms tends to a limit k which is strictly less than 1. In this case the ratio of successive terms tends to zero.

    d) Use one of the previous criteria: left as an exercise which one ...
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