I am confused on what this question means:

Find a series expansion for the expression

x/(1-x) for Abs(x)<1

- Apr 30th 2008, 05:49 AMjgallHow to find a series expansion for x/(1-x) - Please help ASAP & thank you!
I am confused on what this question means:

Find a series expansion for the expression

x/(1-x) for Abs(x)<1 - Apr 30th 2008, 05:54 AMMoo
Hello,

$\displaystyle \frac{x}{1-x}=x \cdot \frac{1}{1-x}=x \cdot \lim_{n \to \infty} \frac{1-x^n}{1-x}^{\color{red}*}=x \cdot \sum_{k=0}^\infty x^k=\dots$

$\displaystyle {\color{red}*} \ : \ |x|<1$, $\displaystyle \lim_{n \to \infty} x^n=0$ - Apr 30th 2008, 05:55 AMtopsquark
That depends on where you are taking an expansion about.

Typically this means a Maclaurin series for the function, that is to say a Taylor series about x = 0.

-Dan