Concept explainers
The sequence is convergent and the series is convergent.
Answer to Problem 9E
The sequence is convergent. the series is convergent.
Explanation of Solution
Given information: The sequence is
Definitions:
Monotone increasing: A sequence
Monotone decreasing: A sequence
Given sequence,.
Now we find
From the above definition, we have
Thus,
Hence,
From the above definition , the sequence is monotone increasing .
Definition of a bounded sequence: A sequence
Now let,
To justify that the guess is correct.
In order that this inequality may be true we should have
Hence, the given sequence is bounded.
Since, the sequence is bounded and monotone increasing
then the sequence is convergent.
Given,
Take limit both side, we have
So the series is convergent.
Chapter 8 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- 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