I have been given the question: "Find the laurent series of $1/(1-z^3)$". No other information.
The question was posed in the process of finding the series' residual and in the answer I can see that there's a simple pole at $z=1$. However, just from the question itself there is no information on which point I should be expanding it. In that case, I expanded about $z = 0$ which results in a series without any poles. Of course, I notice the singularity at $z=1$ and could have made the substitution $u=z-1$ and expanded from there. Is this the general method for a Laurent series? I would have thought the expansion would be about $z=0$ if there is no other information?
In addition, I have tried to find the Laurent series about $z=1$ but am not getting the right answer.
My method: let $u = z-1$:
$f(u) = 1/(1-(u+1)^3) = 1 + (u+1)^3 + (u+1)^6 + ...$
Does the binomial expansion not work for this?