To calculate:The number of terms of the series needed to add in order to get the sum to indicated accuracy?
Answer to Problem 16E
The given series is convergent and the six terms we needed to add in order to get the sum to the indicated
Explanation of Solution
Given information:
Concept Used:
Alternating Series Estimation Theorem:
If
(i)
(ii)
Then the series is convergent and
Calculation:
The series is
For series convergent use alternating series test
Here,
Then
(i)
(ii)
So, by this we can say that the given series is convergent.
For sum to the indicated accuracy use alternating series estimation
Notice that
And
By the alternating series estimation theorem then
This error of less than
So, the six terms we needed to add in order to find the sum to the indicated
Conclusion:
The given series is convergent and the six terms we needed to add in order to get the sum to the indicated
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