Hi could anyone help me with this past exam question (we weren't provided answers)

Find the Laurent series expansion of $f(z)=\frac{e^z}{(z-1)^2}$ for $|z-1|>0$ about $z=1$

I have tried to answer it but unsure if it is right?:

If this is incorrect please could you point me in the right direction? Thanks:)


It's fine. But such a Laurent series is usually expressed as$$\sum_{n=-2}^\infty\frac e{(n+2)!}(z-1)^n,$$so that the exponents of the $(z-1)$'s are equal to $n$.


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