Concept explainers
To find:The geometric series that express the repeating decimal
Answer to Problem 40E
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 in the series
The values are obtained as
Find the sum of the geometric series
Therefore, the sum of the geometric series
Conclusion:
Thus, the repeating decimal
Chapter 10 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
Additional Math Textbook Solutions
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
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University Calculus: Early Transcendentals (3rd Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus and Its Applications (11th Edition)
Precalculus (10th Edition)
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