##\boxed{
\textbf{Problem 3: Find the Laurent series of } f(z) = \frac{z+1}{z^3(z^2-2)} \text{ for:}
\quad \text{(1) } 0 < |z| < 1 \quad \text{(2) } 1 < |z| < +\infty
}##
**Partial Fraction Decomposition**
We begin with the partial fraction decomposition:
$$f(z) = \frac{z+1}{z^3(z^2-2)} =...