Find a power series for f(x) = (1-x)/(1+x).
I got (-2)^n*x^n as an answer, but my answer sheet gives me a much more complicated answer??

Question

Find a power series for f(x) = (1-x)/(1+x). 
I got (-2)^n*x^n as an answer, but my answer sheet gives me a much more complicated answer??

anonymous · Answer

check first that ur answer might be a simplified version of the"complicated" version,

kirbykirby · Answer

I'm not too sure cause the answer in the book is:
-1/3 * (sum from n=1 to oo) of [(-1)^n*2*(x-2)^n]/[3^(n+1)]

kirbykirby · Answer

I thought it was simple. I did this myself: 
1-x+x
------ = 1/(1+2x)
1+x+x

= 1/ (1-(-2x)) for |-2x|<1

so f(x) = (sum from n=0 to inf) of (-2x)^n = (-2)^n*x^n