Consider the function $$f(x) = \frac{x}{1-3 x}.$$ Give the Taylor series for $f(x)$ for values of $x$ near 0.
$f(x) = \displaystyle \sum_{n=0}^\infty$
Give the open interval of convergence for this Taylor series.

(Note: Give your answer in interval notation.)

---

Give the series expansion of $f(x)$ for very large values of $x$ (i.e., in powers of $1/x$).
$f(x) = \displaystyle \sum_{n=0}^\infty$
Give the domain of convergence of this series.

(Note: Give your answer in interval notation.)