Taylor Expansion

1. Dec 24, 2006

phalanx123

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

2. Dec 24, 2006

Galileo

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

3. Dec 24, 2006

Hurkyl

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