In view of the previous exercise, it may be surprising that a subseries of the harmonic series in which about one in every five terms is deleted might converge. A depleted
harmonic series is a series obtained from
removing any term 1/n if a given digit, say 9. appears in the decimal expansion of is. Argue that this depleted harmonic series converges by answering the following questions.
a. How many whole numbers ii have d digits?
b. How many d-digit whole numbers h(d). do not contain 9 as one or more of their digits?
c. That is the smallest d-digit number m(d)?
d. Explain why the deleted harmonic series is bounded by
e. Show that
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Calculus Volume 2
Additional Math Textbook Solutions
Calculus Volume 1
Introductory Statistics
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Mathematics All Around (6th Edition)
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)