Hi

Complex Analysis....

Problem:

Find the Laurent series for $\displaystyle f(z)=\frac{z^{2}}{z^{2}-1} $ about the point $\displaystyle z_{0}=1 $

I got that $\displaystyle f(z)=1+\frac{1}{2}\cdot \frac{1}{z-1}-\frac{1}{2}\cdot \frac{1}{z+1} $ , which I wrote as $\displaystyle 1+\frac{1}{2}\cdot \frac{1}{z-1}+\frac{1}{4}\cdot \sum_{k=0}^{\infty}\left(\frac{z-1}{4}\right)^{k} $

Need some input.

I guess all the terms need to be expressed as powers of $\displaystyle (z-1)$ .

Thx