From f6de0afa90c5d85125192f55ea1baeb923ee8ae6 Mon Sep 17 00:00:00 2001 From: arc Date: Fri, 26 Sep 2025 12:42:34 -0600 Subject: [PATCH] vault backup: 2025-09-26 12:42:34 --- education/math/MATH1220 (calc II)/Sequences.md | 9 +++++++++ 1 file changed, 9 insertions(+) diff --git a/education/math/MATH1220 (calc II)/Sequences.md b/education/math/MATH1220 (calc II)/Sequences.md index 65ae417..69f6f18 100644 --- a/education/math/MATH1220 (calc II)/Sequences.md +++ b/education/math/MATH1220 (calc II)/Sequences.md @@ -39,3 +39,12 @@ Remember, L'Hospital's rule states that: # Series Vocabulary: A **series** is another name for a sum of numbers. + +## Properties +You can break a series into *partial sums*: +$$\sum_{n=1}^\infty a_n = a_1 + 1_2 + a_3 + ...$$ +Given the above series, we can define the following: +- $S_1 = a_1 = \sum_{i=1}^\infty a_i$ +- $S_2 = a_1 + a_2 = \sum_{i=1}^2 a_i$ +- $S_n = a_1 + a_2 + ... = \sum_{i=1}^n a_i$ +- \ No newline at end of file