Bounded and Unbounded Sequences
Big Idea:
When we study sequences, one of the most important questions we can ask is: "Does this sequence stay within some fixed range, or does it eventually escape every boundary we try to set?" This leads us to the concepts of bounded and unbounded sequences.
📌 What is a Sequence?
Recall that a sequence is an ordered list of numbers following a specific rule. We write a sequence as $\{a_n\}$ where $n = 1, 2, 3, \ldots$ For example:
- $a_n = \frac{1}{n}$ gives us $1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \ldots$
- $a_n = 2n$ gives us $2, 4, 6, 8, \ldots$