# The Alternate series Test

What is the alternate series test?

A series test that alternates series (also called the Leibniz test) is used to determine whether two series are convergent. This test does not determine whether they diverge, however. First, we need to understand what convergence and divergence are.

What is a convergent series?

There is something called a convergent series, which is an infinite series that sums to a finite number. As an example famous convrergent series is:

\sum_{n=1}^\infty\frac1{n^2}=\frac{\pi^2}6

convergent series

The sum of these convergent series is \frac{\pi^2}6 What is the process? In general, the p-series test is sufficient to determine whether the series are convergent but requires a lot of calculations.

What is divergent series?

divergent series is an infinite series where the sum is infinity. For example, the series

\sum_{n=1}^\infty\;n^2=1+4+9+…=\infty

Divergent series