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Series & The Divergence Test | Calculus 2 Lesson 20 - JK Math
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Infinite Series & The Divergence Test (Calculus 2 Lesson 20)
In this video we learn about the concept of series and a couple ways to determine their convergence/divergence. Simply put, a series is the sum of the terms of a sequence. We can determine the convergence of a series by looking at the sequence of partial sums for the series. If that sequence converges, then the series converges, but if the sequence diverges then the series also diverges. Additionally, we look at the Divergence Test which is a method used to quickly determine if a series diverges by use of a limit. We look at several examples and explain the solution step by step.
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 Series?
2:35 Partial Sums
6:45 Definition of Convergent & Divergent Series
7:56 Example - 1/(n^2+n)
15:05 Example - 3
19:25 Limit of nth Term of a Convergent Series (Theorem)
22:09 The Divergence Test
23:48 Example - (8n+1)/(2n-3)
25:44 Example - 2^n
26:42 Example - ln(n)/n
29:34 Outro
⚡️Math Products I Recommend⚡️
⚡️Textbooks I Use⚡️
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(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 the concept of series and a couple ways to determine their convergence/divergence. Simply put, a series is the sum of the terms of a sequence. We can determine the convergence of a series by looking at the sequence of partial sums for the series. If that sequence converges, then the series converges, but if the sequence diverges then the series also diverges. Additionally, we look at the Divergence Test which is a method used to quickly determine if a series diverges by use of a limit. We look at several examples and explain the solution step by step.
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 Series?
2:35 Partial Sums
6:45 Definition of Convergent & Divergent Series
7:56 Example - 1/(n^2+n)
15:05 Example - 3
19:25 Limit of nth Term of a Convergent Series (Theorem)
22:09 The Divergence Test
23:48 Example - (8n+1)/(2n-3)
25:44 Example - 2^n
26:42 Example - ln(n)/n
29:34 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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