The n-th term test, also known as the divergence test, is a method used to determine the convergence or divergence of an infinite series. It states that if the limit of the n-th term of a series does not approach zero as n approaches infinity, then the series diverges. In simpler terms, if the terms of the series do not get smaller and closer to zero, the series cannot sum to a finite value. However, if the limit of the n-th term is zero, the test is inconclusive. This means that the series may either converge or diverge, and further tests, such as the ratio test or integral test, may be needed to draw a conclusion.