What will be the Taylor series and the radius of the convergence of $\frac{1+x}{1-x}$ $\frac{1+x}{1-x}$, well it's pretty similar to the geometric series, which is $$1+x+x^2+x^3+...=\sum_{n=0}^{\infty} x^n=\frac{1}{1-x}$$ So if I multiple $$\sum_{n=0}^{\infty} x^n$$ by $x$ can I get the Taylor-series(which is in this case the Maclaurian series?

$\textbf{Hint}:$ $$\frac{1+x}{1-x} = \frac{2}{1-x} - 1 \ \ \ \text{(Why?)}$$
