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Math Help - Determine whether the series converge.

  1. #1
    Junior Member
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    Victoria, Australia
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    Determine whether the series converge.

    I need some help in tackling this problem. Im unsure what test i should use to determine whether this series converges or not. I thinking maybe the comparison test?

    (Sum of) n=1, infinity ncosn / n+5
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  2. #2
    Senior Member
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    Feb 2010
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    ( \sum^\infty {n\cos n \over n+5} you mean?)

    \Big|{n\cos n \over n+5}\Big| = \Big|{n\over n + 5}\Big||\cos n| = \Big|{n+5-5\over n+5}\Big||\cos n| =\Big|1-{5\over n + 5}\Big||\cos n|. Does this go to 0 as n\to\infty? If not, then the series diverges.

    edit: oops, lost the cosine heh
    Last edited by maddas; April 10th 2010 at 08:18 PM.
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