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education/math/MATH1220 (calc II)/Sequences.md
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@@ -99,3 +99,7 @@ The above series converges if all three of the following hold true:
- Series decreases: $a_n \ge a_{n+1}$ for all $n$ - Series decreases: $a_n \ge a_{n+1}$ for all $n$
- $\lim_{n\to\infty} a_n = 0$ 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
Then if the series converges absolutely then the sum converges.