Ok, so this is just a question about clarification. I never learned this in class, so I was hoping someone could explain a small technicality.
The question is Find the Luarent Series of 1/(1-z^2).
I know how to do this. You can do it many ways, but I just first split it up into 1/(1-z)(1+z). Then I found that 1/(1+z) = 1/(2-(1-z)), and I just wrote out the series, divided by 1-z to get the Laurent sreies of
1/(1-z^2) = -1/[2(z-1)]+1/4-1/8(z-1)+1/16(z-1)^2-...
This should be right (but please correct me if I am wrong)
However, the question then asks what happens when |z-1| > 2? I assume when |z-1| > 2, this series is no longer converging? Is that the case? Otherwise, why would they ask this?
It seems to be when |z-1| > 2, the terms are like 1/4, 1/4, 1/4, and getting bigger?
So I am confused. What am I suppose to write for the Laurent series then? Infinity?