Representation of Functions as Power Series

[mateomy]

Find a power series representation for the function and determine the interval of convergence.

$$f(x)=\frac{1+x}{1-x}$$

This is one of the few problems in this section that I am getting stuck on. I know that I can relate it to the form of;

$$\frac{1}{1-(x)}$$

...but after that I don't know what to do with the numerator. Do I move the whole thing over to the right side of the Sigma? So lost, so utterly, utterly lost...-Thanks!

 

[jbunniii]

Try breaking it apart into the sum of two fractions.

 

[mateomy]

Will do. (So bummed that evaded me.)

Thanks a ton!

 

[HallsofIvy]

If you go ahead and do the division, you get
(x+1)/(1- x)= -1+ 3/(1- x). Now think "geometric series".