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.
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.
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.
an
an = 0
