Power series for $(a+x)^{-1}$ Is it possible to write the following expression in terms of power series?
$$ (a+x)^{-1}=\sum\limits_{k =  - \infty }^\infty  {{b_k}{x^k}} $$
where $0 < a < 1$ and $0 < x < 1$.

It can be turned into geometric series:
$$\frac{1}{a+x} = \frac{1}{a} \cdot \frac{1}{1-\left(-\frac{x}{a}\right)} = \frac{1}{a}\cdot\sum\limits_{k=0}^{\infty}\left(-\frac{x}{a}\right)^k$$
which converges whenever $|x| < |a|$.
