To show: The given series is convergent and the sum is less than 90.
Answer to Problem 15P
The series
Explanation of Solution
Given:
The given series is as:
Consider the series whose terms are the reciprocals of the positive integers that can be written in base
Calculation:
Consider the series:
This is the series whose terms of the reciprocals of the positive integers and written in base
Group the terms according to their number of digits in the denominators of the series.
Here,
Each term in
Therefore
Each term in
Therefore
Each term in
Therefore
Similarly in
Therefore,
This series represents a geometric series
And the sum of the series is
From the series
Here,
Therefore the series
Sum of the series is
Therefore
hence
Therefore the series
Chapter 8 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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