# Power expansion

## Homework Statement

I am trying to do our the review exam our teacher posted to study for a test and I am having difficulty trying to figure out where to start and what to do. Our teacher lost me when he was explaining this section. Please help!

## Homework Equations

Write the power expansion for a given function.

x
-------------
(1-x)(1-x^2)

## The Attempt at a Solution

I wasn't sure where to start or what I need to do!

did u try F.O.I.L?(first outer inner last) i believe that is all it is asking

Thanks! But that is not what he is looking for. I need to come up with a summation. One example he worked for us in class was e^(-x^2) = summation (-1)^n [(x^(2n))/n!].

HallsofIvy
Homework Helper
Since this is in the "Calculus and Beyond" section I would rather interpret that as expanding the function in a power series. One way to do that is to find the Taylor's series for the function. Another way is to use the fact that
$$\sum_{n=0}^\infty r^n= \frac{1}{1- r}$$
to interpret 1/(1- x) and 1/(1-x2) as geometric series with r= x and r= x2. Multiply those together (be careful with that) and multiply the result by x (easy).

Sorry to be so dense but I really have hit a wall where this concept is concerned. I understand what you are saying but not sure what you meant to do next. I really need to understand this concept as I have a test coming up! Thanks!

HallsofIvy