From 7f18e40ccb0cc09058fbd45cea0e522d7c7ecb81 Mon Sep 17 00:00:00 2001 From: arc Date: Mon, 22 Sep 2025 14:16:22 -0600 Subject: [PATCH] vault backup: 2025-09-22 14:16:22 --- education/math/MATH1220 (calc II)/Sequences.md | 11 +++++++++++ 1 file changed, 11 insertions(+) create mode 100644 education/math/MATH1220 (calc II)/Sequences.md diff --git a/education/math/MATH1220 (calc II)/Sequences.md b/education/math/MATH1220 (calc II)/Sequences.md new file mode 100644 index 0000000..4430b64 --- /dev/null +++ b/education/math/MATH1220 (calc II)/Sequences.md @@ -0,0 +1,11 @@ +A sequence is defined as an ordered list of numbers. +- Sequences are ordered, meaning two sequences that contain the same values but in a different order are not equal. +- Sequences can be infinite if a rule is defined, i.e $\{1, 1, 1, 1, ...\}; a_i = 1$ + +# Behavior +- A sequence is considered **increasing** if $a_n$ is smaller than $a_{n+1}$ for all $n$. +- A sequence is considered **decreasing** if $a_n$ is greater than or equal to $a_{n+1}$ for all $n$. +- 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: +$