To find: A geometric series for the function
Answer to Problem 55E
The nth term formula for the given function is
Explanation of Solution
Given:
The function is
Concept used:
The mathematical expression of infinite geometric series in general is written as
The convergence test of series states that the geometric series converges if
Furthermore, the convergence test of geometric series also ensures that the convergent infinite geometric series
Calculation:
The given function is
The given function fits the formula for infinite geometric series
The values are obtained as
Write the mathematical expression of infinite geometric series in this form
The nth term formula for the given function can be expressed as follows:
Here, the initial term is
The convergence test of geometric series states that the geometric series converges if
Therefore, the value of
Find the interval of convergence with
Therefore, the interval of convergence is
Conclusion:
Thus, the nth term formula for the given function is
Chapter 10 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
Additional Math Textbook Solutions
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Introductory Statistics
Thinking Mathematically (6th Edition)
Elementary Statistics (13th Edition)
Calculus: Early Transcendentals (2nd Edition)
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