# Newton-Mercator Series/Examples

### Newton-Mercator Series: $\ln 2$
The Newton-Mercator Series for $x = 1$ converges to the natural logarithm of $2$:
 $\ds \sum_{n \mathop = 1}^\infty \frac {\paren {-1}^\paren {n - 1} } n$ $=$ $\ds 1 - \frac 1 2 + \frac 1 3 - \frac 1 4 + \dotsb$ $\ds$ $=$ $\ds \ln 2$