An alternating series is an infinite series of the form:

or:

with

## Alternating Series Test

The theorem known as the "Leibniz Test," or the alternating series test, tells us that an alternating series will converge if the terms

Proof: Suppose the sequence

Since

Example:

## Alternating Harmonic Series

The first fourteen partial sums of the alternating harmonic series (black line segments) shown converging to the natural logarithm of 2 (red line).