In this section we briefly state two results concerning series an with terms an that are not necessarily ≥ 0. The first result has to do with absolute convergence and the second with alternating series.

  1. A series an is said to converge absolutely if | an| converges. It is a theorem that if any series converges absolutely, then it also converges.
  2. A series an is said to be alternating if the an alternate between being positive and negative. If an is an alternating series such that | an+1|≤| an| for all n≥1 and an = 0, then an converges. This is called the alternating series test.