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Ratio Test | Calculus 2 Lesson 29 - JK Math
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How to Use the Ratio Test for Series (Calculus 2 Lesson 29)
In this video we learn how to determine if a series converges or diverges by using the Ratio Test. The ratio test is particularly useful for series involving factorials and exponential parts. We will take the limit as n approaches infinity of the ratio between two terms of the series a_(n+1) and a_n, and depending on the result of that limit, we can either make a conclusion about the convergence or divergence of the series, or the test will be inconclusive and we will need to use another test on the series.
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 What is The Ratio Test?
2:19 Example - 4^n/n!
9:06 Example - n*(10/9)^n
13:46 Example - ((-1)^(n+1)*(n+2))/(n*(n+1))
29:33 Example - (5^(n+3)*n^2)/7^n
35:49 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 using the Ratio Test. The ratio test is particularly useful for series involving factorials and exponential parts. We will take the limit as n approaches infinity of the ratio between two terms of the series a_(n+1) and a_n, and depending on the result of that limit, we can either make a conclusion about the convergence or divergence of the series, or the test will be inconclusive and we will need to use another test on the series.
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 What is The Ratio Test?
2:19 Example - 4^n/n!
9:06 Example - n*(10/9)^n
13:46 Example - ((-1)^(n+1)*(n+2))/(n*(n+1))
29:33 Example - (5^(n+3)*n^2)/7^n
35:49 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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