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Coefficient in a Power Series

  1. Sep 29, 2009 #1
    1. The problem statement, all variables and given/known data

    The function
    [tex]f(x)=\frac{1}{1+x^{9}}[/tex]
    can be expanded in a power series
    [tex]\sum^{\infty}_{0} a_{n}x^{n}[/tex]
    with center c = 0.
    Find the coefficient
    [tex]a_{27}[/tex]
    of
    [tex]x^{27}[/tex]
    in this power series.

    2. The attempt at a solution

    I can get to:

    [tex]\sum^{\infty}_{0} (-1)^{n}(-x^{9})^{n}[/tex]

    which I think is right, but I'm not sure how to find [tex]a_{27}[/tex]. We didn't talk about it in class.
     
    Last edited: Sep 29, 2009
  2. jcsd
  3. Sep 29, 2009 #2

    Dick

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    You don't want (-1)^n and (-x^9)^n to both have a '-' in them do you? What are the first few terms in the series when you write them out? a_27 is the coefficient of x^27, which is the n=3 term in your series. What is it?
     
  4. Sep 29, 2009 #3
    Ohhh, okay, I think I understand now. So the coefficient would just be [tex](-1)^{3}=-1[/tex]?
     
  5. Sep 29, 2009 #4

    Dick

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    Right.
     
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