Alternating series

An alternating series is a series in which the number of links are alternately positive and negative, that is, a series of the form:

Wherein said positive real numbers. Often it is additionally required that the sequence is monotonically decreasing.

A simple example of an alternating series is the alternating harmonic series

In contrast to the harmonic series

In the sign of the terms of the series does not change. Probably the most well-known alternating rows are the series expansions of sine and cosine:

To study the convergence of these series, the Leibniz criterion can be used.