How can I find the first few terms of the Laurent series for

[Jonobro]

Homework Statement

For each of the following functions find the first few terms of each of the Laurent series about the origin, that is, one series for each annular ring between singular points. Find the residue of each function at the origin.

The function is...

1/(z*(z-1)(z-2)^2)

Homework Equations

N/A

The Attempt at a Solution

I did partial fraction expansion and got 1/(z-1)- 1/(4z) - 3/(4(z-2)) + 1/(2(z-2)^2) but am not sure where to go from here... Any help would be appreciated.

 

[Geofleur]

The $-1/(4z)$ term already has the form you want. So how about Taylor expanding the other terms about $z = 0$ to make them into power series in $z$?