1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  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
    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


    User Avatar
    Science Advisor
    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!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: The coefficients of a power series for natural log
  1. Power series of logs (Replies: 1)

  2. Power Series for log z (Replies: 6)