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

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1. Oct 19, 2015

Jonobro

1. The problem statement, all variables and given/known data
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)

2. Relevant equations
N/A

3. 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.

2. Oct 19, 2015

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 $z$?