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Monotonic & Bounded Sequences | Calculus 2 Lesson 19 - JK Math
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How to Determine Convergence of Monotonic & Bounded Sequences (Calculus 2 Lesson 19)
In this video we learn about how to determine if a sequence converges based on if it s monotonic and bounded. We discuss what it means for a sequence to be monotonic and bounded, and how to determine each of those potential features of a sequence. We go through each definition and explain thoroughly with various examples.
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 The Goal of This Lesson
1:02 Monotonic Sequences (Definition)
4:05 Monotonic Sequences (Visually)
6:35 Example - 4n/(n+3)
12:44 Example - (2/3)^n
17:07 Alternative Method (Derivative)
21:50 Bounded Sequences
24:16 Example - n
27:14 Example - 1/n
30:41 Putting it all Together!
31:31 Example - 1/n^3
38:34 Example - (-1)^n
42:41 Outro
⚡️Math Products I Recommend⚡️
⚡️Textbooks I Use⚡️
⚡️My Recording Equipment⚡️
(Commissions earned on qualifying purchases)
Find me on social media:
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.
In this video we learn about how to determine if a sequence converges based on if it s monotonic and bounded. We discuss what it means for a sequence to be monotonic and bounded, and how to determine each of those potential features of a sequence. We go through each definition and explain thoroughly with various examples.
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 The Goal of This Lesson
1:02 Monotonic Sequences (Definition)
4:05 Monotonic Sequences (Visually)
6:35 Example - 4n/(n+3)
12:44 Example - (2/3)^n
17:07 Alternative Method (Derivative)
21:50 Bounded Sequences
24:16 Example - n
27:14 Example - 1/n
30:41 Putting it all Together!
31:31 Example - 1/n^3
38:34 Example - (-1)^n
42:41 Outro
⚡️Math Products I Recommend⚡️
⚡️Textbooks I Use⚡️
⚡️My Recording Equipment⚡️
(Commissions earned on qualifying purchases)
Find me on social media:
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.
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