From 303d2c2087e9fece9bbe57d56761154461bf612a Mon Sep 17 00:00:00 2001 From: arc Date: Wed, 1 Oct 2025 12:44:00 -0600 Subject: [PATCH] vault backup: 2025-10-01 12:44:00 --- education/math/MATH1220 (calc II)/Sequences.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/education/math/MATH1220 (calc II)/Sequences.md b/education/math/MATH1220 (calc II)/Sequences.md index b3a4bd2..8d3783d 100644 --- a/education/math/MATH1220 (calc II)/Sequences.md +++ b/education/math/MATH1220 (calc II)/Sequences.md @@ -85,4 +85,6 @@ $$ = \sum_{n=1}^\infty \frac{35}{7}(\frac{1}{7})^{n-1}* 2^{n-1} = \sum_{n = 1}^\ $$\sum_{n=1}^{\infty}35(7^{-n} * 2^{n-1}) = \dfrac{\frac{35}{7}}{1-\frac{2}{7}}$$ # Divergence Test -If $\lim_{n \to \infty} a_n \ne 0$ then $\sum_{a} \ No newline at end of file +**If $\lim_{n \to \infty} a_n \ne 0$ then $\sum_{n=1}^\infty a_n$diverges.** + +The divergence test only tells us that if the limit does not equal zero, then the series diverges. If the limit is zero, it doesn't necessarily mean the series converges. \ No newline at end of file