Definition:Mercator's Constant

Theorem
The series defined as:
 * $\displaystyle \sum_{n \mathop = 1}^\infty \frac {\left({-1}\right)^\left({n - 1}\right)} n = 1 - \frac 1 2 + \frac 1 3 - \frac 1 4 + \cdots$

is known as the alternating harmonic series.

Also see

 * Definition:Harmonic Series