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Math Help - Determine whether the series is AC .. etc

  1. #1
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    Determine whether the series is AC .. etc

    Hi
    am studying for my incomplete exam after 10 days ..
    I have problem with this question
    http://www.sci.kuniv.edu.kw/content/...-April2007.pdf
    Question 4-b

    I know i will say |an| < an without cos 2n

    and then ? which test i will use ?
    I tested it with a couple with tests and i failed
    help :/
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  2. #2
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    (2n)^n \cdot 2^{-n^2} \cdot \cos(2n) \le (2n)^n \cdot 2^{-n^2} = \left(\frac{2n}{2^n}\right)^n<br />

    nth root test ...

    \lim_{n \to \infty} \sqrt[n]{\left(\frac{2n}{2^n}\right)^n}

    \lim_{n \to \infty} \frac{2n}{2^n} = 0

    series converges
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