Calculus BC: Series
Series With Positive and Negative Terms
In this section we briefly state two results concerning series
a
n
with terms
a
n
that are not necessarily
≥ 0
. The first result has to do with
absolute convergence and the second with alternating series.
- A series
a
n
is said to converge absolutely if
| a
n|
converges. It is a theorem that if any series converges
absolutely, then it also converges.
- A series
a
n
is said to be alternating if the
a
n
alternate
between being positive and negative. If
a
n
is an alternating series
such that
| a
n+1|≤| a
n|
for all
n≥1
and
a
n = 0
,
then
a
n
converges. This is called the alternating series test.
