From 694ea2e219cea6dae427d8453545980e88c82c99 Mon Sep 17 00:00:00 2001 From: arc Date: Mon, 22 Sep 2025 14:21:22 -0600 Subject: [PATCH] vault backup: 2025-09-22 14:21:22 --- education/math/MATH1220 (calc II)/Sequences.md | 12 +++++++++++- 1 file changed, 11 insertions(+), 1 deletion(-) diff --git a/education/math/MATH1220 (calc II)/Sequences.md b/education/math/MATH1220 (calc II)/Sequences.md index 4430b64..d850c13 100644 --- a/education/math/MATH1220 (calc II)/Sequences.md +++ b/education/math/MATH1220 (calc II)/Sequences.md @@ -8,4 +8,14 @@ A sequence is defined as an ordered list of numbers. - Sequences exist that do not fall into either category, i.e, $a_n = (-1)^n$ - If the terms of a sequence grow $\{a_n\}$ get arbitrarily close to a single number $L$ as $n$ grows larger, this is noted by writing: -$ +$$\lim_{n\to\infty} a_n = L$$ OR +$$ a_n \to L \text{ as } n \to \infty $$ + +and say that $a_n$ *converges* to $L$. If no $L$ exists, we say $\{a_n\}$ *diverges*. + +# Properties of Sequences +> The below properties assume two sequences are defined, $a_n \to L$ and $b_n \to M$ +1. $a_n + b_n \to L + M$ +2. $C*a_n \to CL$ +3. $a_n b_n \to LM$ +4.