alternating series

An alternating series is a series of the form

\sum_{i=0}^{\infty}(-1)^{i}a_{i}

\sum_{i=0}^{\infty}(-1)^{i+1}a_{i}

where $(a_{n})$ is a non-negative sequence. Loosely, this is just a series where the “alternate” between positive and negative.

For convergence issues, see the following entry: alternating series test (http://planetmath.org/AlternatingSeriesTest).