Calculate the sum S (z) of the power series for z on the convergence disk.

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Calculate the sum S (z) of the power series for z on the convergence disk $\sum_{n=1}^{\infty}\frac{(-1)^n}{n}(z-i)^n$

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Hint: $\ln(1+z)=\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}nz^n$, for $\mid z\mid\lt1$.