alternating series

An alternating series is a series of the form

$$\sum _{i=0}^{\mathrm{\infty }}{(-1)}^i{a}_i$$

or

$$\sum _{i=0}^{\mathrm{\infty }}{(-1)}^{i+1}{a}_i$$

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).