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Math Help - Find the limit of sequence

  1. #1
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    Find the limit of sequence

     \lim_{n \to \infty} a_ {n}

    a_ {n} =\sqrt[n]{|cos n|}
    Last edited by radian92; November 12th 2011 at 09:14 AM.
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  2. #2
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    Re: Find the limit of sequence

    Can we assume n is a whole number? If we can, every even value might be a problem.

    What ideas have you?
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  3. #3
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    Re: Find the limit of sequence

    Sure, n is the integer.The limit is 1, but i can't prove it.
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Find the limit of sequence

    Maybe it can help to write \lim_{n \to \infty} \sqrt[n]{\cos(n)} as \lim_{n \to \infty} \cos(n)^{\frac{1}{n}}=e^{\lim_{n\to \infty} \frac{\ln[\cos(n)]}{n}}=...
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  5. #5
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    Re: Find the limit of sequence

    Why don't we care that it's intermittent? What do you think, OP?
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