MathNet 2016-part-01 — 184 problems (EN–VI) Question 15

For an integer $m \ge 3$ set $S(m) = 1 + \frac{1}{3} + \dots + \frac{1}{m}$ (the fraction $1/2$ does not participate in the sum). Let $n \ge 3$ and $k \ge 3$. Compare the numbers $S(nk)$ and $S(n) + S(k)$.