# Find a power series for ln(5-x)

• May 19th 2013, 12:17 PM
Coop
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
• May 19th 2013, 01:06 PM
Coop
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.