Question 92
Let $n$ be a positive integer, and let $a_1, \dots, a_n$ be pairwise distinct positive integers. Show that
$$
\sum_{k=1}^{n} \frac{1}{[a_1, \dots, a_k]} \lt 4,
$$
where $[a_1, \dots, a_k]$ is the least common multiple of the integers $a_1, \dots, a_k$.
$$
\sum_{k=1}^{n} \frac{1}{[a_1, \dots, a_k]} \lt 4,
$$
where $[a_1, \dots, a_k]$ is the least common multiple of the integers $a_1, \dots, a_k$.