Example of Using the Monotonic Sequence Theorem | Calculus 2 скачать в хорошем качестве

Example of Using the Monotonic Sequence Theorem | Calculus 2

We use the monotonic sequence theorem to show a recursively defined sequence converges. We'll use mathematical induction to prove the sequence is increasing (monotone) and then we'll use proof by induction to prove the sequence is bounded above by 5. This will allow us to use the monotonic sequence theorem (also called the monotone convergence theorem) to conclude the sequence has a limit, then some algebra will allow us to figure out what the limit is. #calculus2 #calculus Join Wrath of Math to get exclusive videos, lecture notes, and more:    / @wrathofmath   Calculus 2 Course:    • Calculus 2   Calculus 2 Exercises:    • Calculus 2 Exercises   Get the textbook for this course! https://amzn.to/3PieD1M ★DONATE★ ◆ Support Wrath of Math on Patreon:   / wrathofmathlessons   ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Outro music by Crayon Angel: https://crayon-angel.bandcamp.com/ Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● TikTok:   / wrathofmathedu   ● X: https://x.com/wrathofmathedu ● Facebook:   / wrathofmath   0:00 Intro 0:27 The Recursive Sequence 1:22 Using Monotone Sequence Theorem 1:51 Proving the Sequence is Increasing 3:51 Prove the Sequence is Bounded 5:41 Finding the Limit 7:33 Conclusion