Root Test | Calculus 2 Lesson 30 - JK Math

How to Use the Root Test for Series (Calculus 2 Lesson 30)

In this video we learn how to determine if a series converges or diverges by using the Root Test. The root test is particularly useful for series involving powers of n. We will take the limit as n approaches infinity of the nth root of the absolute value of the nth term of a series, 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 Root Test?
1:43 Example - (1/n)^n
5:13 Example - 1/5^n
7:50 Example - e^(2n)/n^n
10:26 Example - ((4n+3)/(2n-1))^n
13:41 Example - n^n/3^(2+3n)
19:07 Example - ((-1)^(n+1)*2^(n+4))/(n+1)^n
24:16 Example - 1/n^3
32:42 Outro

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