This test involves some assumptions about the positive sequence.

Given a series $\sum _{n=0}^{\mathrm{\infty }}(-1{)}^n{a}_n$

If the following 3 requirements are met:

1. $a_n$ is positive for $n\ge 0$
2. $a_n$ is decreasing for $n\ge 0$
3. $a_n$ converges to 0 ($\underset{n\to \mathrm{\infty }}{lim}{a}_n=0$)

Then the series $\sum _{n=0}^{\mathrm{\infty }}(-1{)}^n{a}_n$ converges
Warning:
This test only determines convergence, but not whether it is absolutely or conditionally convergent.

If the requirements are not met the test is inconclusive.