Find the largest domain where $z-z^2+z^3...$ has

Question

Let $f(z)=z-z^2+z^3...$, $|z|<1$. Find the largest domain where $f$ can be extend analytically.

The radius of convergence of $f$ is obviously $1$. Any help is appreciated.

Answer 1

Hint: $$ \frac1{1-x} = 1 + x + x^2 + \cdots $$ for $|x| < 1$.