Question 48
Let $x_{1}, x_{2}, \ldots, x_{n}$ be positive integers such that no one of them is an initial fragment of any other (for example, $12$ is an initial fragment of $12$, $125$ and $12405$). Prove that
$$
\frac{1}{x_{1}}+\frac{1}{x_{2}}+\cdots+\frac{1}{x_{n}}\lt 3
$$
$$
\frac{1}{x_{1}}+\frac{1}{x_{2}}+\cdots+\frac{1}{x_{n}}\lt 3
$$