How to tell if a sequence is bounded?
Understand the Problem
The question is asking for the criteria or methods to determine whether a given mathematical sequence is bounded. A bounded sequence is one where all its terms lie within a fixed range, meaning there exists a number that limits the values of the terms in the sequence.
Answer
A sequence is bounded if its terms lie within a finite interval.
A sequence is bounded if it has both an upper and a lower bound, meaning all of its terms lie within a finite interval.
Answer for screen readers
A sequence is bounded if it has both an upper and a lower bound, meaning all of its terms lie within a finite interval.
More Information
A sequence that lacks either an upper or a lower bound, meaning the terms can grow indefinitely in at least one direction, is called unbounded.
Tips
Be sure to clearly identify both an upper and lower bound. Missing either bound means the sequence isn't fully bounded.
Sources
- How to Determine if a Sequence is Bounded using the Definition - youtube.com
- Bounded Sequences | Calculus II - courses.lumenlearning.com
- Definition of a bounded sequence - Mathematics Stack Exchange - math.stackexchange.com
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