vault backup: 2025-09-22 14:16:22

education/math/MATH1220 (calc II)/Sequences.md

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+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:
+$