The first few terms in the Laurent series for \(\frac{1}{{\left( {z - 1} \right)\left( {z - 2} \right)}}\) in the region \(1 \le \left| z \right| \le 2\) and around z = 1 is
1
\(\frac{1}{2}\left[ {1 + z + {z^2} + \ldots } \right]\left[ {1 + \frac{z}{2} + \frac{{{z^2}}}{4} + \frac{{{z^3}}}{8} + \ldots } \right]\,\)
2
\(\frac{1}{{1 - z}} - z - {\left( {1 - z} \right)^2} + {\left( {1 - z} \right)^3} + \ldots \,\)
3
\(\frac{1}{{{z^2}}}\left[ {1 + \frac{2}{z} + \frac{4}{{{z^2}}} + \ldots } \right]\left[ {1 + \frac{2}{z} + \frac{4}{{{z^2}}} + \ldots } \right]\,\)
4
\(2\left( {z - 1} \right) + 5{\left( {z - 1} \right)^2} + 7{\left( {z - 1} \right)^3} + \ldots \,\)
5
Not Attempted