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education/math/MATH1220 (calc II)/Sequences.md
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@@ -100,6 +100,10 @@ The above series converges if all three of the following hold true:
- $\lim_{n\to\infty} a_n = 0$ as_
This test does not provide any guarantees about divergence i.e if if the test fails, the series does not necessarily diverge.
A sequence a_n converges absolutely if sum `|a_n|` converges
A sequence $a_n$ *converges absolutely* if $\sum |a_n|$ converges
Then if the series converges absolutely then the sum converges.
Then if the *series converges* absolutely then the sum converges.
## Examples
> Does the series $\sum_{n=1}^\infty (\frac{(-1)^n}{n+5}$ conditionally converge, absolutely converge, or diverge?
1. $\sum_{n=1}^\infty|\frac{(-1)^n}{n+5}| = \sum_{n=1}^\infty \frac{1}{n+5}$