Find Laurent series expansion for $\frac{z}{2-z}$ on $2< \vert z \vert<\infty$.

Question

So I know I need to find the series which includes negative indices. I divided and get

$$\frac{z}{2-z}=-1+\frac{2}{2-z}=-1+\frac{1}{1-\frac{z}{2}}.$$

So for the power series I get

$$-1+\sum_{n=0}^\infty \bigg(\frac{z}{2}\bigg)^n.$$

So is this it? OR...? Is $a_{-1}=-1$?