diff --git a/education/math/MATH1220 (calc II)/Sequences.md b/education/math/MATH1220 (calc II)/Sequences.md index d590641..a038d5b 100644 --- a/education/math/MATH1220 (calc II)/Sequences.md +++ b/education/math/MATH1220 (calc II)/Sequences.md @@ -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. \ No newline at end of file +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. $\sum_{n=1}^\infty|\frac{(-1)^n}{n+5}| = \sum_{n=1}^\infty \frac{1}{n+5}$