How to find the limit of a recursively defined sequence

In this video, I show you how to use induction and the monotone sequence theorem to find the limit of a recursively defined sequence.
ADDENDUM (Oct 6, 2024): Once the sequence is shown to be increasing (and hence has all positive terms), induction is not necessary to show boundedness, because a_(n-1)＞ 0 implies that a_n = 4 - 1/a_(n-1) ＜ 4 - 0 = 4 for all n.