Geometric Series | Calculus 2 Lesson 22 - JK Math

How to Determine the Convergence of a Geometric Series (Calculus 2 Lesson 22)

In this video we learn about a special type of series known as a geometric series and how to determine its convergence. A geometric series is a series who terms are found by multiplying each term by the same value that we call the common ratio. We discuss how to identify a geometric series by first looking at geometric sequences, and then explain how to determine the convergence by finding the nth partial sum and developing a formula. Additionally, we look at an application of geometric series that allows us to rewrite a repeating decimal as a fraction.

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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 Geometric Sequence?
5:59 What is a Geometric Series?
8:22 Geometric Series Definition
9:31 Partial Sums of a Geometric Series
18:04 Convergence of a Geometric Series
23:34 Definition of Convergence of a Geometric Series
24:34 Example - 5/3^n
27:55 Example - (5/2)^n
29:16 Example - 3(1/2)^n starting at n=2
36:18 Example - Express 0.4 Repeating as a Fraction
41:45 Outro


📝 Examples Video:    • Geometric Series Examples | Calculus 2 - J...  

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📺 Calculus 2 Playlist:    • Calculus 2  

📺 Calculus 1 Playlist:    • Calculus 1  


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