The first four terms of the Taylor series expansion of \(f\left( z \right) = \frac{{z + 1\;}}{{\left( {z - 3} \right)\left( {z - 4} \right)}},\) when z = 2 is

• A. \(\frac{{11}}{4}\left( {z - 2} \right) + \frac{{27}}{8}{\left( {z - 2} \right)^2} + \frac{{59}}{{16}}{\left( {z - 2} \right)^3} + \ldots \)
• B. \(\frac{{11}}{4}\left( {z + 2} \right) - \frac{{27}}{8}{\left( {z - 2} \right)^2} - \frac{{59}}{{16}}{\left( {z + 2} \right)^3} + \ldots \)
• C. \(\frac{3}{2} + \frac{{11}}{4}\left( {z - 2} \right) + \frac{{27}}{8}{\left( {z - 2} \right)^2} + \frac{{59}}{{16}}{\left( {z - 2} \right)^3} + \ldots \)
• D. \(\frac{3}{2} - \frac{{11}}{4}\left( {z - 2} \right) - \frac{{27}}{8}{\left( {z - 2} \right)^2} - \frac{{59}}{{19}}{\left( {z - 2} \right)^3} + \ldots \)