Chapter 6 - Section 6.1 - The Basics of Counting - Exercises - Page 396: 13

$n$

Each of the strings, 1(length 1), 11(length 2), 111(length 3), 1111(length 4), ... , 111...111(length n) have a length "not exceeding n" and consist entirely of 1s. In fact, these are the only strings which satisfy both of these conditions. Therefore the number of strings of length "not exceeding n" and consist entirely of 1s = n Note that if we count the empty string the answer will be $n+1$ but we have been asked to not count it in the question