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Convergence of a Sequence Defined Recursively

In this video, I will discuss how to determine the convergence of a sequence defined recursively. To navigate the lecture, you may use the following timecodes: 0:00 Intro 1:40 Definition of an increasing sequence 2:06 Definition of a decreasing sequence 2:29 Definition of a monotone sequence 3:04 Checking whether a sequence is monotone (Algebra approach) 4:53 Checking whether a sequence is monotone (Calculus approach) 6:36 Checking whether a sequence is monotone (Algebra approach) 8:13 Checking whether a sequence is monotone (Calculus approach) 9:21 Checking whether a sequence is monotone 10:47 Definition of a sequence bounded above 11:39 Definition of a sequence bounded below 12:01 Definition of a bounded sequence 12:35 Checking whether a sequence is bounded 14:49 Checking whether a sequence is bounded 16:20 Checking whether a sequence is bounded 17:13 Checking whether a sequence is bounded 18:40 The 5-word theorem 21:21 Example of using the 5-word theorem 22:34 Example of using the 5-word theorem 23:07 Checking convergence of a sequence defined recursively 32:54 Finding the limit of a convergent sequence defined recursively 35:16 Checking convergence of a sequence defined recursively 40:43 Finding the limit of a convergent sequence defined recursively 41:24 Outro