The Laurent series expansion of the function \(f\left( z \right) = \frac{1}{{{e^z} - 1}}\) valid in the region 0 < |z| < 2, is given by
1
\(f\left( z \right) = \frac{1}{z} - \frac{1}{2} + \frac{1}{3}z - \frac{1}{{120}}{z^3} + \ldots \)
2
\(f\left( z \right) = \frac{1}{z} + \frac{1}{2} - \frac{1}{3}z + \frac{1}{{120}}{z^3} + \ldots \)
3
\(f\left( z \right) = \frac{1}{z} - \frac{1}{2} + \frac{1}{{12}}z - \frac{1}{{720}}{z^3} + \ldots \)
4
\(f\left( z \right) = \frac{1}{z} - \frac{1}{2} + \frac{1}{{12}}z - \frac{1}{{120}}{z^3} + \ldots \)