Concept explainers
To Find : If the sequence is convergent or divergent using a graph of sequence and then find the limit of the sequence.
Answer to Problem 40E
The sequence is convergent and it’s limit is zero.
Explanation of Solution
Given information : The nthterm of the sequence is given by,
By substituting the value of n in equation (1), gives the first five terms as
Table formed with the obtained values is shown below.
The graph of sequence is obtained as shown below, with n in x - axis and an in y - axis .
n | an |
1 | |
2 | |
3 | |
4 | |
5 |
Above graph shows that the sequence is convergent sequence. And its limit is 0.
Proof of limit of an ,
Therefore,
Thus,
The obtained sequence is convergent and it’s limit is zero.
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