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Homework Help: The coefficients of a power series for natural log

  1. May 22, 2008 #1
    1. The problem statement, all variables and given/known data

    The function f(x) =ln(10 - x) is represented as a power series in the form

    f(x) = (sum from 0 to infinity) of c[tex]_{n}[/tex]x[tex]^{n}[/tex]

    Find the first few coefficients in the power series.

    3. The attempt at a solution

    I know how to find the coefficients in a normal looking taylor series (for example, 3/(1 - 2x)^2 or something) but I don't have any idea where to start for a natural log...

    for the record

    C0 = 2.30258509299

    C1 = -0.1

    C2 = -0.005

    C3 = -0.000333333333333

    C4 = -2.5E-05

    Radius of convergence = 10

    Help?
     
  2. jcsd
  3. May 22, 2008 #2
    There's a really nice trick for finding power series for functions of the form [tex]f(x) = ln(a+x)[/tex].

    When you take the derivative of f, you get
    [tex]f'(x)=\frac{1}{a+x}.[/tex]
    Since f'(x) expands to a geometric series, all you need to do find that and then take it's integral from 0 to x.
     
  4. May 22, 2008 #3

    Dick

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    Homework Helper

    You are only asked to find the first few coefficients in the power series. I think you are doing quite well. What's the problem?
     
  5. May 22, 2008 #4
    No, I was able to find the answer afterwards by getting the question wrong. I don't know how to derive the answer from the question.

    Well, I do now though. Thank you!
     
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