Monotonic & Bounded Sequences - Calculus 2

Another way to decide if a sequence converges or not is by determining if it is monotonic and bounded. If these two conditions are met, we can conclude that a sequence converges without ever needing to use a limit. But what does it mean for a sequence to be monotonic and bounded?

A monotonic sequence is sequence whose terms are either increasing or decreasing. This means that each subsequent term gets larger than the previous term, or each subsequent term gets smaller than the previous term. If the terms of a sequence do not either increase or decrease, but increase AND decrease as they progress, the sequence is not monotonic.

A bounded sequence is a sequence whose terms will never go above a certain value (bounded above) and will never go below a certain value (bounded below). It's important to note that if a sequence is only bounded above or only bounded below that it is not bounded. It needs to be both bounded above and below in order to meet the requirements of being bounded.

How to determine if a sequence is monotonic and bounded, and as result, if it converges, is the focus of this lesson in Calculus 2, and so let's get right to it!

In this lesson, you will learn:

• How to determine if a sequence is monotonic (increasing or decreasing)
• How to determine if a sequence is bounded (above and below)
• How to determine if a sequence converges based on if it is monotonic and bounded

I hope you find this video to be helpful!

-Josh