The Taylor series expansion of \(\dfrac{1}{z-2}, |z|< 1\) is
1
\(-\dfrac{1}{2}\left(1-\dfrac{z}{2} + \dfrac{z^2}{4}- \dfrac{z^3}{8}...\right)\)
2
\(-\dfrac{1}{2}\left(1+\dfrac{z}{2} + \dfrac{z^2}{4}+ \dfrac{z^3}{8}...\right)\)
3
\(-\dfrac{1}{2}\left(1-\dfrac{z}{2} - \dfrac{z^2}{4}+ \dfrac{z^3}{8}...\right)\)
4
\(x -\dfrac{1}{2}\left(1+\dfrac{z}{2} - \dfrac{z^2}{4}- \dfrac{z^3}{8}...\right)\)