Taylor series of log(1+z)

Theorem

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.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.1.24