What is the alternating harmonic series?

The alternating harmonic series is an infinite series in mathematics that converges conditionally. It is not an absolutely convergent series.

An alternating series is a mathematical series wherein the consecutive terms alternate from a positive value to a negative value. If a series comprises only positive terms, it is said to be a divergent series, an example of which is a harmonic series. If a series contains some negative values, the positive terms are canceled and the series converges. A method of testing whether an alternating series is convergent is to use the Alternating Series Test. The test proves that an alternating harmonic series does not absolutely converge but conditionally converges.