# alternating series

An alternating series is a series of the form

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

or

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

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).

Title alternating series AlternatingSeries 2013-03-22 12:27:05 2013-03-22 12:27:05 mathcam (2727) mathcam (2727) 6 mathcam (2727) Definition msc 40-00 alternating series test LeibnizsTheorem ProofOfLeibnizsTheorem AlternatingSeriesTest