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education/math/MATH1220 (calc II)/Sequences.md
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@@ -97,4 +97,5 @@ $$ \sum_{n=1}^\infty (-1)^{n+1}a_n = a_1 - a_2 + a_3 - a_4 $$
The above series converges if all three of the following hold true: The above series converges if all three of the following hold true:
- $a_n > 0$ - $a_n > 0$
- 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.