# inversion of formal series

• October 16th 2010, 04:50 AM
excellents
inversion of formal series
Hello!

I have a formal power series: $f(x) = 1 + x + x^2 + x^3 + ...$ and I have to find a series $g(x)$: $g(x) = {1 \over f(x)}$.

Using the formula found on Wikipedia Formal power series - Wikipedia, the free encyclopedia I've got this result: $g(x) = 1 - x$. I see this result as very strange. How can I check it?
• October 16th 2010, 05:11 AM
chisigma
For $|x|<1$ is...

$\displaystyle f(x)=\frac{1}{1-x} = 1+x+x^{2}+x^{3} + ...$ (1)

... so that is [simply]...

$\displaystyle \frac{1}{f(x)} = 1-x$ (2)

Kind regards

$\chi$ $\sigma$