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Math Help - [SOLVED] need a urgent help in sum of series

  1. #1
    saggi_twist
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    [SOLVED] need a urgent help in sum of series

    Hi.
    can anyone give me a complete solutions to the problem below..
    Need urgently

    Find The sum of series of,
    <br />
cos(3x) + \sum_{n=1}^{\infty}\frac{(-1)^n cos^3(3^nx)}{3^n}<br />

    Need an urgent help to solve these kind of series problem..I need the full solution part
    Last edited by saggi_twist; January 10th 2008 at 07:15 AM. Reason: Need an urgent help to solve these kind of series problem..
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by saggi_twist View Post
    Hi.
    can anyone give me a complete solutions to the problem below..
    Need urgently


    Find the sum of series
    Cos3x –((1/3)*( Cos(3x)*Cos(3x)*Cos(3x))+((1/9)* Cos(9x)*Cos(9x)* Cos(9x)) – ((1/27)*Cos(27x)*Cos(27x)*Cos(27x))+…..


    Need an urgent help to solve these kind of series problem..
    Can't you try to give this to us in a clearer manner? That is a very messy series. It's nearly impossible to figure out.
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  3. #3
    GAMMA Mathematics
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    Quote Originally Posted by janvdl View Post
    Can't you try to give this to us in a clearer manner? That is a very messy series. It's nearly impossible to figure out.
    cos(3x) + \sum_{n=1}^{\infty}\frac{(-1)^n cos^3(3^nx)}{3^n}
    Last edited by colby2152; January 8th 2008 at 07:50 AM. Reason: x's as n's?
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  4. #4
    Super Member wingless's Avatar
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    I think it's
    Cos(3x)-\frac{1}{3} Cos(3x)^3+\frac{1}{9} Cos(9x)^3-\frac{1}{27} Cos(27x)^3+\frac{1}{81} Cos(81x)^3\text{...}<br />

    Which can be shown in sum notation,

    Cos(3x) + \sum_{n=1}^{\infty}(-\frac{1}{3})^n Cos^3(3^{n}x)
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  5. #5
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    Is there a summation formula for, \sum_{n=0}^{\infty} \frac{(-1)^n x^{3^n}}{3^n} ~ |x|\leq 1?
    I was able to reduce your sum to that sum.
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