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

find the Laurent series for f(z) = 1/(z(z-1)(z-2)) on the annulus between 1 and 2. with the origin as center.

**2. Relevant equations**

**3. The attempt at a solution**

so i found the partial fraction decomposition of this function and it turns out to be f(z) = 1/2z + -1/(z-1) + 1/(2(z-2)). In order to find the Laurent series do I just Taylor expand each of my 3 different decomposition around their singularities? However, their singularities are not contained on the annulus so this doesnt seem to make much sense. I am unsure how to proceed from this spot.