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Concept explainers
Provide notes on an infinite sequence, the meaning of the convergent sequence, and the meaning of divergent sequence with example.
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Explanation of Solution
The infinite sequence of numbers is a function whose domain is the set of positive integers.
Example:
Consider the following sequence is
Provide the sequence of each term as follows.
The formula for
Hence, the formula for
Provide the sequence to be converge and diverge as shown below.
The sequence
If no such number L exists, we say that
If
Example:
For converge sequence:
Consider the nth formula for the sequence function is
Find the limit of sequence as follows:
The limit of the sequence is 2.
Hence, the sequence is converge.
For diverge sequence:
The nth formula for the sequence function is
Find the limit of sequence as follows:
The limit of the sequence does not exists.
Therefore, the sequence is diverge.
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Chapter 9 Solutions
University Calculus: Early Transcendentals (4th 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
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