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Direct Comparison Test | Calculus 2 Lesson 25 - JK Math
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How to Use the Direct Comparison Test for Series (Calculus 2 Lesson 25)
In this video we learn how to determine if a series converges or diverges by directly comparing it to a similar series whose convergence is known. This method is known as the Direct Comparison Test and is one of two different companions tests that can be used for determining the convergence or divergence of a series (second test in next lesson). In most cases this comparison test will be used for series who share similar features to geometric series and p-series where comparisons can easily be made.
This video 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 Why Do We Need Comparison Tests?
4:10 The Direct Comparison Test
6:13 Why The Direct Comparison Test Works (Visually)
9:20 Example - 1/(3^n+5)
14:57 Example - 1/(2+n^4)
19:31 Example - 1/(sqrt(n)+1)
30:03 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 how to determine if a series converges or diverges by directly comparing it to a similar series whose convergence is known. This method is known as the Direct Comparison Test and is one of two different companions tests that can be used for determining the convergence or divergence of a series (second test in next lesson). In most cases this comparison test will be used for series who share similar features to geometric series and p-series where comparisons can easily be made.
This video 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 Why Do We Need Comparison Tests?
4:10 The Direct Comparison Test
6:13 Why The Direct Comparison Test Works (Visually)
9:20 Example - 1/(3^n+5)
14:57 Example - 1/(2+n^4)
19:31 Example - 1/(sqrt(n)+1)
30:03 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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