In the neighborhood of z = 1, the function f(z) has a power series expansion of the form $${\text{f}}\left( {\text{z}} \right) = 1 + \left( {1 - {\text{z}}} \right) + {\left( {1 - {\text{z}}} \right)^2} + \,...$$
Then f(z) is

A. $$\frac{1}{{\text{z}}}$$

B. $$\frac{{ - 1}}{{{\text{z}} - 2}}$$

C. $$\frac{{{\text{z}} - 1}}{{{\text{z}} + 2}}$$

D. $$\frac{1}{{2{\text{z}} - 1}}$$

Answer: Option A