Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(2) An interesting fact is that the Root Test (stated at the end of the previous problem) is stronger than the Ratio Test. Proving this fact would require showing two things: First, one can show that any time the Ratio Test limit exists and equals some L then the Root Test limit also exists and equals the same L. Second, one can find examples of series where the Root Test works but the Ratio Test does not. Your task in this problem is to do the second thing above. To be more specific, find an example of a series a, such that • lim Vlan[ exists and equals a number less than 1, meaning the series converges absolutely by the Root Test, and • lim does not exist. Give a brief explanation why your example satisfies the above two properties.

(2) An interesting fact is that the Root Test (stated at the end of the previous problem) is stronger than the Ratio Test. Proving this fact would require showing two things: First, one can show that any time the Ratio Test limit exists and equals some L then the Root Test limit also exists and equals the same L. Second, one can find examples of series where the Root Test works but the Ratio Test does not. Your task in this problem is to do the second thing above. To be more specific, find an example of a series a, such that • lim Vlan[ exists and equals a number less than 1, meaning the series converges absolutely by the Root Test, and • lim does not exist. Give a brief explanation why your example satisfies the above two properties.

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section: Chapter Questions
Problem 23RE: Use the formula for the sum of the first ii terms of an arithmetic series to find the sum of the...
See similar textbooks
icon
Related questions
Question
(2) An interesting fact is that the Root Test (stated at the end of the previous problem) is stronger than the Ratio Test. Proving this fact would require showing two things: First, one can show that any time the Ratio Test limit exists and equals some L then the Root Test limit also exists and equals the same L. Second, one can find examples of series where the Root Test works but the Ratio Test does not. Your task in this problem is to do the second thing above. To be more specific, find an example of a series a, such that • lim Vlan[ exists and equals a number less than 1, meaning the series converges absolutely by the Root Test, and • lim does not exist. Give a brief explanation why your example satisfics the above two properties.
Transcribed Image Text:(2) An interesting fact is that the Root Test (stated at the end of the previous problem) is stronger than the Ratio Test. Proving this fact would require showing two things: First, one can show that any time the Ratio Test limit exists and equals some L then the Root Test limit also exists and equals the same L. Second, one can find examples of series where the Root Test works but the Ratio Test does not. Your task in this problem is to do the second thing above. To be more specific, find an example of a series a, such that • lim Vlan[ exists and equals a number less than 1, meaning the series converges absolutely by the Root Test, and • lim does not exist. Give a brief explanation why your example satisfics the above two properties.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer