I'm trying to compute the Laurent series of $f(z) = 1/z^2$ about the point $z_0=1$. Looking at my notes, it appears that I need to compute a series for $|z-1| < 1$ and one for $|z-1|>1$, due to the singularity at the point $1$.
Could someone show me how to compute each of these series? I'm a bit confused on where to begin.
EDIT: The problem says to "Write all Laurent series of the following functions on annuli centered at $z_0$," so I feel like there should be two series: one valid for $|z-1|<1$ and another valid for $|z-1|>1$.