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AP Calculus AB/BC
A bounded sequence is a sequence in which all the terms are limited within a certain range. In other words, there are upper and lower bounds that the terms of the sequence do not exceed.
A convergent sequence is a bounded sequence that also approaches a specific value as its terms continue. It has a limit.
A divergent sequence is a bounded sequence that does not approach any specific value as its terms continue. It does not have a limit.
A monotonic sequence is a bounded sequence in which the terms either always increase or always decrease as you move along the sequence.