Hello!

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

Using the formula found on Wikipedia Formal power series - Wikipedia, the free encyclopedia I've got this result: $\displaystyle g(x) = 1 - x$. I see this result as very strange. How can I check it?