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Converging & Diverging Sequences | Calculus 2 Lesson 18 - JK Math

How to Determine the Convergence of Sequences (Calculus 2 Lesson 18) In this video we learn about sequences as they relate to mathematics and ultimately calculus. We introduce what sequences are and how they function. After introducing sequences as a concept, we then take a look at what it means for a sequence to converge and how to determine if a sequence converges or diverges by using limits. This includes looking at the squeeze theorem for sequences which allows us to determine the convergence of sequences that would otherwise be quite difficult with a regular limit. 🖥️ Join My Membership Site: https://www.jkmathematics.com/plus This series is designed to help students understand the concepts of Calculus 2 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture! Calculus 2 requires a solid understanding of calculus 1, precalculus, and algebra concepts and techniques. This includes limits, differentiation, basic integration, factoring, equation manipulation, trigonometric functions, logarithms, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first! Video Chapters: 0:00 What is a Sequence? 2:32 Example - Terms of 2n 3:38 Example - Terms of (-1)^n 5:26 Example - Terms of n/(n+1) from n=0 to ∞ 7:12 Example - Terms of 3n/(n+2) from n=2 to 5 9:31 Recursively Defined Sequence 12:06 Pattern Recognition For Sequences 17:10 Example - nth Term For {-1, 1/2, -1/6, 1/24, -1/120, …} 22:15 Convergence of Sequences 24:30 Limit of a Sequence 25:30 Example - Convergence of 5-3/n 27:01 Example - Convergence of 7n+1 28:24 Example - Convergence of 9n/(3n-2) 31:11 Example - Convergence of 1+(-1)^n 33:36 Example (Part 1) - Convergence of (-1)^n/n 35:30 Squeeze Theorem For Sequences 37:06 Example (Part 2) - Convergence of (-1)^n/n 40:12 Outro 📝 Examples Video:    • Converging & Diverging Sequences Examples ...   ⏩ Next Lesson:    • Monotonic & Bounded Sequences | Calculus 2...   📺 Calculus 2 Playlist:    • Calculus 2   📺 Calculus 1 Playlist:    • Calculus 1   🌐 Visit My Website: https://www.jkmathematics.com ⚡️Math Products I Recommend⚡️ Graphing Calculator: https://amzn.to/3XuUcB9 Non-Graphing Calculator: https://amzn.to/46hHJ7E Financial Calculator: https://amzn.to/3CRe9s4 Graphing Paper: https://amzn.to/46mAfAr College Rule Paper: https://amzn.to/3NOJaTN My Favorite Pencil: https://amzn.to/3NOFMIB My Favorite Erasers: https://amzn.to/3PumUQB Calculus Workbook: https://amzn.to/3r8SnNP ⚡️Textbooks I Use⚡️ Calculus 1 & 2: https://amzn.to/3PzfI5F Calculus 3: https://amzn.to/46rSy76 Financial Mathematics: https://amzn.to/3ppIVW0 ⚡️My Recording Equipment⚡️ iPad Air: https://amzn.to/3phEug1 Apple Pencil (Gen 2): https://amzn.to/3Nl45MM Tablet Desk Stand: https://amzn.to/4420rPh External Hardrive: https://amzn.to/44pkEyh (Commissions earned on qualifying purchases) Find me on social media: Facebook:   / jkmathematics   Twitter:   / jk_mathematics   Instagram: @jk_mathematics Found this video to be helpful? Consider giving this video a like and subscribing to the channel! Thanks for watching! Any questions? Feedback? Leave a comment! -Josh from JK Math #calculus Disclaimer: Please note that some of the links associated with the videos on my channel may generate affiliate commissions on my behalf. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.