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Math Help - Limit of a strange sequence

  1. #1
    Newbie Femto's Avatar
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    Limit of a strange sequence

    Define sequence by a_0 = 1 and a_(n + 1) = cos(a_(n)/2). Given that |cos(x) - cos(y)| < (or equal to) |x - y| use this to show that cos(a_n/2) -> cos(a/2).

    Not exactly sure how to get this. I'm probably being inane here. This question comes under Cauchy sequences..
    Last edited by Femto; November 11th 2012 at 09:13 AM.
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  2. #2
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    Re: Limit of a strange sequence

    Quote Originally Posted by Femto View Post
    Define sequence by a_0 = 1 and a_(n + 1) = cos(a_(n)/2). Given that |cos(x) - cos(y)| < (or equal to) |x - y| use this to show that cos(a_n) -> cos(a/2).
    Not exactly sure how to get this. I'm probably being inane here. This question comes under Cauchy sequences..

    @Femto please review your post.
    Is it \left(\cos\left(a_n\right)\right)\to\cos\left( \frac{a}{2} \right)~?

    If so, what is a in that?
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  3. #3
    Newbie Femto's Avatar
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    Re: Limit of a strange sequence

    Quote Originally Posted by Plato View Post
    @Femto please review your post.
    Is it \left(\cos\left(a_n\right)\right)\to\cos\left( \frac{a}{2} \right)~?

    If so, what is a in that?
    No it's not. I've written it wrong - it should be cos(an/2)
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  4. #4
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    Re: Limit of a strange sequence

    Quote Originally Posted by Femto View Post
    No it's not. I've written it wrong - it should be cos(an/2)
    What should be cos(an/2)? That makes no sense.
    Please rewrite the entire question.
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  5. #5
    Newbie Femto's Avatar
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    Re: Limit of a strange sequence

    Done
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  6. #6
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    Re: Limit of a strange sequence

    Great! But what in the world was "a"? You never did say that!
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