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education/math/MATH1220 (calc II)/Sequences.md
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@@ -94,3 +94,7 @@ Sometimes a series is not continually positive for the entire series, meaning mo
A simple example of an alternating series is: A simple example of an alternating series is:
$$ \sum_{n=1}^\infty (-1)^{n+1}a_n = a_1 - a_2 + a_3 - a_4 $$ $$ \sum_{n=1}^\infty (-1)^{n+1}a_n = a_1 - a_2 + a_3 - a_4 $$
The above series converges if all three of the following hold true:
- $a_n > 0$
- Series decreases: $a_n \ge a_{n+1}$ for all $n$
- $\lim_{n\to\infty} a_n = 0$ as_