Concept explainers
To find:The geometric series that express the repeating decimal
Answer to Problem 41E
The repeating decimal
Explanation of Solution
Given:
The repeating decimal 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 repeating decimal is
Rewrite the repeating decimal
The given function fits the formula for infinite geometric series
Here, the initial term is 1 and each sequential term is multiplied by
The values are obtained as
Find the sum of the geometric series as follows.
Therefore, the sum of the geometric series is
Conclusion:
Thus, the repeating decimal
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic
Additional Math Textbook Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Calculus & Its Applications (14th Edition)
Precalculus Enhanced with Graphing Utilities (7th 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