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 $0 < x < 1$.

$$\frac{1}{1-x}=\sum_{n=0}^\infty x^n$$
$$\frac{1}{1+x}=\sum_{n=0}^\infty (-1)^nx^n$$
$$\frac{1}{1+x/a}=\sum_{n=0}^\infty (-1)^n\left(\frac{x}{a}\right)^n$$
$$\frac{1}{a+x}=\frac1a\sum_{n=0}^\infty (-1)^n\left(\frac{x}{a}\right)^n$$
Convergent for $$\left|\frac{x}{a}\right|<1\implies x<a$$
