Putnam 1964 B1

Let $u_k$ be a sequence of integers, and let $V_n$ be the number of those which are less than or equal to $n$ . Show that if $$\sum_{k=1}^{\infty} \frac{1}{u_k } < \infty,$$ then $$\lim_{n \to \infty} \frac{ V_{n}}{n}=0.$$