In Problems 1–4 find the radius of convergence and interval of convergence for the given power series.
In this problem, we are asked to find the interval and the radius of convergence for the power series.
To find the Radius of convergence, let us use the ratio test.
Thus for the series converges.
Therefore the radius of convergence is .
Now we have to find the interval of convergence.
For that, we have to check whether the series is convergent at the endpoints and .
Therefore at the series becomes
This the series diverges at , by the p series test.
Textbook: A First Course in Differential Equations with Modeling Applications
Author: Dennis G. Zill
The full step-by-step solution to problem: 3E from chapter: 6.1 was answered by , our top Calculus solution expert on 07/17/17, 09:41AM. The answer to “In 1–4 find the radius of convergence and interval of convergence for the given power series.” is broken down into a number of easy to follow steps, and 16 words. A First Course in Differential Equations with Modeling Applications was written by and is associated to the ISBN: 9781111827052. This textbook survival guide was created for the textbook: A First Course in Differential Equations with Modeling Applications, edition: 10. Since the solution to 3E from 6.1 chapter was answered, more than 257 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Convergence, interval, given, Find, power. This expansive textbook survival guide covers 109 chapters, and 4053 solutions.