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Math Help - Evaluate The Following Limit (3).

  1. #1
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    Evaluate The Following Limit (3).

    Hello
    \lim_{n\to\infty} (cos(n))^n
    What the hell is this ?

    I can not do anything
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  2. #2
    MHF Contributor
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    1
    It oscillates from -1 to 0 to 1 and back again.

    For natural k...

    When n=2k\pi,\ Cos(n)=1

    When n=k\pi,\ Cos(n)=-1
    Odd powers of this is -1 and even powers is 1

    When n=k\frac{\pi}{2}, for\ k\ odd,\ Cos(n)=0

    When n = any other value, Cos(n) will be between -1 and 0, or between 0 and 1, hence the infinite power will cause it to go to 0.
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