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  1. #1
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    Post help

    I want to solve this exercises but I can n't ,can you help me please?

    I want to find sum of functions series , and 'i' here is an index.



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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by suliman View Post
    I want to solve this exercises but I can n't ,can you help me please?

    I want to find sum of functions series , and 'i' here is an index.



    Well lets assume that for 1 you mean:

    $\displaystyle s(n)=\sum_{i=1}^n \left( \frac{1}{x^{2i+1}}- \frac{1}{x^{2i-1}}\right)\ \ \ x \in (0,1]$

    ($\displaystyle x$ cannote be $\displaystyle 0$ as then the summands are undefined)

    Then:

    $\displaystyle
    s(n)=\sum_{i=1}^n \frac{1}{x^{2i}} \left( \frac{1}{x}- x\right)
    $

    ...... $\displaystyle =\left( \frac{1}{x}- x\right)\sum_{i=1}^n \frac{1}{x^{2i}}=\left( \frac{1}{x}- x \right) \left( \frac{1-x^{-2(n+1)}}{1-x^{-2}} \right),\ \ \ x \ne 1$

    and $\displaystyle s(n)=0$ if $\displaystyle x=1$

    RonL
    Last edited by CaptainBlack; Aug 5th 2008 at 12:05 AM.
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