Definition:Newton-Mercator Series

Definition
Let $\ln x$ denote the natural logarithm function.

Then:

The series converges to the natural logarithm (shifted by $1$) for $-1 < x \le 1$.

This is known as the Newton-Mercator series.

Also known as
The Newton-Mercator series is also known as the Mercator series, or Mercator's series.

Also see

 * Power Series Expansion for Logarithm of 1 + x for a proof of its convergence