To calculate: The series converges absolutely, converges conditionally, or diverges.
Answer to Problem 31E
The series converges conditionally.
Explanation of Solution
Given information:
Calculation:
Assuming it is intended to be like how wrote it with parentheses here (and not
Alternating series test
The limit of the terms approaches zero.
Each successive term (without the sign) is smaller than the previous term.
So it converges.
(probably useless info: this series
To test for absolute convergence, can drop the
Therefore, the original series converges and it doesn't converge absolutely so it conditionally converges.
Chapter 9 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning