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In this video I review bounded and monotonic sequences as well as the monotonic sequence theorem. A bounded sequence is one in that is bounded above and bounded below. A sequence is bounded above if there is a number that is less than every term in the sequence. Likewise, a sequence bounded below is if there is a number that is larger than every term in the sequence. A monotonic sequence is either always increasing or always decreasing. The monotonic sequence theorem, which I covered in my earlier video, states that a bounded, monotonic sequence is always convergent.
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This video was taken from my earlier video listed below:
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Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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