MathNet 2023-part-04 — 191 problems (EN–VI) Question 9

Show that every positive integer $n$ can be expressed as a sum of positive integers, where the sum of their reciprocals is less than or equal to $4$. For instance, as $5 = 2 + 2 + 1$, we find that $1/2 + 1/2 + 1/1 = 2 \le 4$.