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??

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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??

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

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