5.9 Alternating series test
Alternating series test
Lessons
Notes:
Note *An Alternating series is in the form:
$\sum(1)^nb_n$
or
$\sum(1)^{n+1}b_n$
Where $b^n \geq0$ An alternating series is not limited to these two forms because the exponent on the (1) can vary.
The Alternating Series Test states that if the two following conditions are met, then the alternating series is convergent:
1. $\lim$_{n →$\infty$} $b_n=0$
2. The sequence $b_n$ is a decreasing sequence.
For the second condition, $b_n$ does not have to be strictly decreasing for all $n\geq 1$. As long as the sequence is decreasing for $n$→$\infty$, then that will be sufficient enough.

2.
Convergence of the Alternating Series Test
Show that the following series converge: