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Math Help - Limit of (-1)^n(1/n^3)cos(n^3)

  1. #1
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    Limit of (-1)^n(1/n^3)cos(n^3)

    See http://www.wolframalpha.com/input/?i...+n-%3Einfinity.

    This is a sequence, not a series.

    I need to prove that this converges to 0.

    I have thought about trying a proof by contradiction, and the comparison test (cos(n^3)/n^3) is always smaller than 1/n^3.

    I have thought about breaking up the limit into individual parts, but I still get 0 times a divergent.

    Thank you.
    Last edited by mr fantastic; October 3rd 2009 at 10:59 PM. Reason: Added link tags
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  2. #2
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    Quote Originally Posted by runningeagle View Post
    See - Wolfram|Alpha.

    This is a sequence, not a series.

    I need to prove that this converges to 0.

    I have thought about trying a proof by contradiction, and the comparison test (cos(n^3)/n^3) is always smaller than 1/n^3.

    I have thought about breaking up the limit into individual parts, but I still get 0 times a divergent.

    Thank you.
    Note:
    1. The numerator is bounded for all values of n.
    2. Denominator --> +oo as n --> +oo.
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