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This video introduces recursive sequences and explains how the convergence of recursively defined sequences can be proven using the monotonicity criterion. It also shows how the limit of a recursive sequence can be determined. In both cases, complete induction is helpful and an extensive example helps with better understanding. Recursive sequences can also be put into an explicit form in which all terms of the sequence can be determined directly. This video is the 27th video on sequences, which represent the first of the major topics in analysis. If you liked the video, please leave a like or a free subscription! If you have suggestions for improvement or don't understand something, write it in the comments :)