Complex Analysis: Theory and Applications · Problem 7.3.4

Taylor and Laurent Series — Howell & Matthews

Mathematics — Complex Analysis · laurent-series

Problem

Show that 1−zz−2=−∑n=0∞1(z−1)n\dfrac{1-z}{z-2} = -\displaystyle\sum_{n=0}^{\infty}\dfrac{1}{(z-1)^n} is valid for ∣z−1∣>1|z-1| > 1. Hint: Refer to the solution for Exercise 3a Section 7.2.

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