Putnam 1969 B5

Let $a_1 < a_2 < a_3 < \cdots$ be an increasing sequence of positive integers. Let the series $$\sum_{n=1}^{\infty} \frac{1}{a_n}$$ be convergent. For any number $x$, let $k(x)$ be the number of the $a_n$'s which do not exceed $x$. Find the value of \lim_{x \to \infty} \frac{k(x)}{x}.