I am posting this on behalf of a friend, she just wants confirmation if her working out is correct.
revised working out answer image
Any input is much appreciated
Many Thanks
2026-04-02 19:34:57.1775158497
Complex analysis find the laurent series, is my working out correct?
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The denominator changes abruptly from $1-z$ to $1-(z-1) = 2-z$ with no explanation. Is that two separate problems?
Given the region of convergence, I would assume the denominator should have been $2-z$ originally. Under that assumption...
The final series converges in $|z-1|< 1$ and diverges for $|z-1|>1$, so it's the wrong region.