GATE IN 2021 | Question: 26

Question

$f\left ( Z \right )=\left ( Z-1 \right )^{-1}-1+\left ( Z-1 \right )-\left ( Z-1 \right )^{2}+ \cdots$ is the series expansion of

• A. $\frac{-1}{Z\left ( Z-1 \right )}$ for $\left | Z-1 \right |< 1$
• B. $\frac{1}{Z\left ( Z-1 \right )}$ for $\left | Z-1 \right |< 1$
• C. $\frac{1}{\left ( Z-1 \right )^{2}}$ for $\left | Z-1 \right |< 1$
• D. $\frac{-1}{\left ( Z-1 \right )}$ for $\left | Z-1 \right |< 1$