This is another past exam question, which we have not been given anwers to, so i was hoping someone could check my answer, so i know if i am on the right track.

Find the first three non zero terms of the laurent series on an annulus centred at zero.

f(z)=(1/(z²(1-z)²))

Now the sinularities are at 0, and 1, and they are both double poles.

I did it as follows:

0<|z|<1

(1/(z²(1+(-z)²))=(1/(z²))*∑{n=0}to{∞} zⁿ]

I don't understand what you did here: certainly So you can do Tonio
and i used the binomial theorm to get the cooeficients of z.

This gave me:

(1/(z²))-(2/z)+3-4z

Does any one know a way that i can check my solution, to make sure i have not stuffed it up.