Question

hey guys
I need to turn 1/x² into a series representation.
since i know that 1/x= sum n=0 to infinite of (1-x)^n , I thought of writing it down as a cauchy-product. Here's a link of a picture of how far I got:
http://s7.directupload.net/images/130605/jmaqbvrg.jpg

Unfortunately I have no Idea what the next step is

Answer 1

with what center you want to expand?

Answer 2

I think it was x0=1

Answer 3

with center x=1, you can do this
\[ \frac{1}{x^2} = \frac{1}{(1 - (1-x))^2 } = 1 - 2 (1-x) + (-2)(-3)/2! (1-x)^2 + .. \]
expand binomially

Answer 4

to generalize it
\[ \frac{1}{x^2} = \sum_{n=0}^\infty (-1)^n n(1-x)^n\]
should have a radius of convergence of 1

Answer 5

woops!! looks like i made mistake