Divergence tests are methods used in mathematics to determine whether a series converges or diverges. A series diverges if the terms do not approach zero as the number of terms increases. If the limit of the terms of the series does not equal zero, the series cannot converge. One common divergence test is the n-th term test, which states that if the limit of the terms of a series as n approaches infinity is not zero, the series diverges. This test is simple and provides a quick way to assess the behavior of a series without needing to find its sum.