From 31a847196d1e68d479a7796484c38b47f9e5ac6b Mon Sep 17 00:00:00 2001 From: arc Date: Mon, 13 Oct 2025 15:07:06 -0600 Subject: [PATCH] vault backup: 2025-10-13 15:07:06 --- education/math/MATH1220 (calc II)/Sequences.md | 10 +++++++++- 1 file changed, 9 insertions(+), 1 deletion(-) diff --git a/education/math/MATH1220 (calc II)/Sequences.md b/education/math/MATH1220 (calc II)/Sequences.md index 307eff9..88a795d 100644 --- a/education/math/MATH1220 (calc II)/Sequences.md +++ b/education/math/MATH1220 (calc II)/Sequences.md @@ -130,4 +130,12 @@ where $x$ is a variable. $\sum x^n$ converges when $|x| < 1$ and diverges when $|x| \ge 1$. -The above series is a series of the \ No newline at end of file +The above series is a power series where $a_n = 1$ and $c = 0$. + +## Behavior +The behavior a given power series falls into one of three cases: +1. The series converges on an interval with radius $R > 0$ When this happens, each interval endpoint needs to be checked independently, because the ratio test will always be indeterminate at those points. +2. The series converges for all $x = \mathbb{R}$ +3. + +# Examples