Question 8
Let $1 = a_1 \le a_2 \le \dots \le a_n \le \dots$ be integers such that there are infinitely many positive integers $k$ with $k = \frac{i}{a_i}$ for some $i$.
Show that for every positive integer $n$, there exists a positive integer $j$ such that $n = \frac{j}{a_j}$.
Show that for every positive integer $n$, there exists a positive integer $j$ such that $n = \frac{j}{a_j}$.