10.3 The \(n^{th}\) Term Test for Divergence

Definition: \(n^{th}\) Term Test

If \(\lim_{n \to \infty} a_n \neq 0\) or if the limit does not exist, then the series \(\sum a_n\) diverges.

Note: If the limit is 0, the test is inconclusive; the series might converge or diverge.