Taylor series of log(1+z)

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Theorem[edit]

The following formula holds for $|z| \leq 1$ and $z \neq -1$: $$\log(1+z)=-\displaystyle\sum_{k=1}^{\infty} \dfrac{(-1)^kz^k}{k},$$ where $\log$ denotes the logarithm.

Proof[edit]

References[edit]