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Math Help - proving that a function is monotonic and bounded..

  1. #1
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    proving that a function is monotonic and bounded..

    in this link i written the question and how i tried to solve them

    http://img504.imageshack.us/img504/7371/95405842kw4.gif

    how to finish it??
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by transgalactic View Post
    in this link i written the question and how i tried to solve them

    http://img504.imageshack.us/img504/7371/95405842kw4.gif

    how to finish it??
    You need to prove that a_n=\prod_{k=1}^{n}\frac{k+9}{2k-1} is both monotonic and bounded. Start with solving

    k+9<2k-1\implies 10<k

    So this tells us one thing since all the terms after ten are less than one we may say that \sum_{k=1}^{n}\frac{k+9}{2k-1}<\prod_{k=1}^{10}\frac{k+9}{2k-1}=512 and that \forall{n}>10 a_{n+1}<a_n
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  3. #3
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    by saying that my series is smaller then 1
    you are deciding that its descending.


    why did you decided that its descending??
    maybe its ascending and we should do bigger then 1
    ??
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  4. #4
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    ok i understand the monotonic part

    how to pove that this series is bounded?
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