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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_ - $\lim_{n\to\infty} a_n = 0$ as_
This test does not provide any guarantees about divergence i.e if if the test fails, the series does not necessarily diverge. 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. $\sum_{n=1}^\infty|\frac{(-1)^n}{n+5}| = \sum_{n=1}^\infty \frac{1}{n+5}$