How to know if a sequence is bounded?
Understand the Problem
The question is asking for a method or criteria to determine whether a given sequence of numbers is bounded, meaning it does not go to positive or negative infinity and stays within certain limits.
Answer
A sequence is bounded if all terms fall within fixed upper and lower bounds.
A sequence is bounded if there exist numbers that can serve as both an upper and lower bound, such that all terms of the sequence fall within these bounds.
Answer for screen readers
A sequence is bounded if there exist numbers that can serve as both an upper and lower bound, such that all terms of the sequence fall within these bounds.
More Information
A bounded sequence has both an upper and a lower limit for its values, making sure the sequence does not go to positive or negative infinity.
Tips
A common mistake is failing to find a concrete upper or lower bound. Ensure you verify with precise numbers.
Sources
- Bounded Sequence - Superprof - superprof.co.uk
- Bounded Sequences | Calculus II - Courses.lumenlearning.com. - courses.lumenlearning.com
- How do you prove that a sequence is bounded? - Quora - quora.com
