We are given \(k > 0 \in \mathbb{R}\) and \(a_1, a_2, \ldots, a_n \ge 1 \in \mathbb{N}\) such that

$$ a_1 < a_2 < \cdots < a_n. $$

We want to solve the following equation

$$ \frac{1}{a_1} + \frac{1}{a_2} + \cdots + \frac{1}{a_n} = k. $$