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Math Help - Find a power series for ln(5-x)

  1. #1
    Junior Member Coop's Avatar
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    Find a power series for ln(5-x)

    Hi,

    I need to find the power series for the function ln(5-x).

    Here's what I did,

    \frac{1}{5-x}\implies\frac{1/5}{1-x/5}=\frac{1}{5}+\frac{x}{25}+\frac{x^{2}}{125}+... They are equivalent, correct?

    \int\frac{1/5}{1-x/5}=-[ln|5-x|]=\frac{x}{5}+\frac{x^{2}}{50}+\frac{x^{3}}{375}+..  .

    Then, since that equals -[ln|x-5|],[ln|x-5|]=-\sum_{0}^{\inf}\frac{x^{n+1}}{(n+1)5^{n+1}}

    But the answer key says that there is supposed to be an ln(5) in front of my answer, what did I miss?

    Thanks
    Last edited by Coop; May 19th 2013 at 12:21 PM.
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  2. #2
    Junior Member Coop's Avatar
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    Re: Find a power series for ln(5-x)

    Nevermind, I figured it out. The ln(5) in front of the real answer is the constant from integration.
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