I'm working my way through Needham's Visual Complex Analysis. In $\S 2.3$ he talks about complex power series. He wants to generalize the geometric series; $\sum_{j=0}^{\infty} x^j = 1 + x + x^2 + \dots$ by expanding $1/(a-x)$ about $k$:
$\frac{1}{a-x}=\frac{1}{a-(X+k)} = \frac{1}{a-k}\frac{1}{1-\frac{X}{a-k}}$
where $X = (x-k)$ measures displacement of $x$ from the centre $k$. He then immediately claims
$\frac{1}{a-x}=\sum_{j=0}^{\infty}\frac{X^j}{(a-k)^{j+1}} iff \hspace{3mm} \lvert X \lvert < \lvert a-k \lvert $
I don't understand the last jump. Any clarification would be immensely appreciated! Thanks!