f(z) = (z − 1)−1 − 1 + (z − 1) − (z − 1)2 + ⋯ is the series expansion of

1
\(\frac{-1}{z(z-1)} ~for ~|z - 1| < 0\)
2
\(\frac{1}{z(z-1)}~ for~ |z - 1| < 0\)
3
\(\frac{1}{(z-1)^2} ~for ~|z - 1| < 0\)
4
\(\frac{-1}{(z-1)} ~for~ |z - 1| < 0\)

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