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