Taylor Expansion for ln(1+x)/(1-x) About x=0

phalanx123 · Dec 24, 2006

Hi I wonder if there is a simpler way to obtain the first three non-zero terms of Taylor Expansion for the function [tex]\frac{Ln(1+x)}{1-x}[/tex] about x=0?

I differentiated it directly, but it was such a nightmare to do

. So I am wondering if there is a simpler way to do it?

Galileo · Dec 24, 2006

You can take the Taylor expansions of 1/(1-x) and ln(1+x) and multiply those. Gather coefficients etc.

Hurkyl · Dec 24, 2006

Or, you could compute the Taylor series for Ln(1+x), and then divide by 1-x.

Taylor Expansion for ln(1+x)/(1-x) About x=0

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