I'm a bit stuck on this question:
Identify the annular regions centered on $z = 0$ in which the function :
$$f(z) = \frac{1}{z(z+1)}$$
is analytic. Find the Laurent series about $z=0$ which is valid for each of the regions.
I've found the Taylor series for $\displaystyle \frac{1}{z+1}$ which gives me a principle part of $\displaystyle \frac{1}{z}$, so I assume the region will then be $0 < |z| < 1$. I'm not sure how to progress from there. Do I then find the Taylor series for $\displaystyle \frac{1}{z}$?
Thanks in advance.