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education/math/MATH1220 (calc II)/Sequences.md
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@ -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, $a_n = (-1)^n$ - 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: - 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.