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Math Help - Sequence

  1. #1
    Junior Member
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    Aug 2009
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    62

    Sequence

    Hi,

    (\forall n \in \mathbb{N})\ \ U_n=\frac{n^2}{2^n}

    I should calculate \lim_{n\to +\infty}  \frac{U_{n+1}}{U_n}
    and I must deduct that there is a n_0 in \mathbb{N} such as :  (\forall n \ge n_0) \ \frac{U_{n+1}}{U_n} < \frac{3}{4}.

    For the limit, it's equal to \frac{1}{2}, but for the deduction, idon't know anything.

    Can you help me please???

    Thanks.
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  2. #2
    Banned
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    Oct 2009
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    Quote Originally Posted by lehder View Post
    Hi,

    (\forall n \in \mathbb{N})\ \ U_n=\frac{n^2}{2^n}

    I should calculate \lim_{n\to +\infty} \frac{U_{n+1}}{U_n}
    and I must deduct that there is a n_0 in \mathbb{N} such as :  (\forall n \ge n_0) \ \frac{U_{n+1}}{U_n} < \frac{3}{4}.

    For the limit, it's equal to \frac{1}{2}, but for the deduction, idon't know anything.

    Can you help me please???

    Thanks.

    !!! The deduction is only the very application of the definition of limit!! For example, take \epsilon=\frac{1}{8} ...

    Tonio
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