The divergence test is a method used in calculus to determine whether a series diverges, meaning it does not converge to a finite limit. If the terms of a series do not approach zero as the number of terms increases, the series is guaranteed to diverge. This is a quick way to identify non-converging series without needing to find their sum. To apply the divergence test, one examines the limit of the terms of the series as they approach infinity. If the limit is not zero, or if it does not exist, the series diverges. However, if the limit is zero, the test is inconclusive, and further analysis is needed.