Problem 15
Page 632
Section: Focus on Problem Solving
Chapter 8: Infinite Sequences and Series
Given information
The series whose terms are the reciprocals of the positive integers that can be written in base 10 notation without using the digit 0.
Step-by-step explanation
Consider the series:
This is the series whose terms of the reciprocals of the positive integers and written in base 10 notation without using the digit 0.
Group the terms according to their number of digits in the denominators of the series.
Each term in 
is less than or equals to 
.
Therefore 
terms for and each term which are less than or equal to
Each term in 
is less than or equals to 
.
Therefore 
terms for and each term which are less than 
.
Each term in is less than or equals to 
.
Therefore 
terms for 
and each term which are less than 
.
Similarly in 
, 
terms for and each term which are less than 
.