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.

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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


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