1975 IMO 第 5 题

Let $M$ be the set of all positive integers that do not contain the digit 9 (base 10). If $x_{1}, \ldots, x_{n}$ are arbitrary but distinct elements in $M$, prove that $$\sum_{j=1}^{n} \frac{1}{x_{j}}<80$$

令 $M$ 为所有不包含数字 9(以 10 为底)的正整数的集合。如果$x_{1}, \ldots, x_{n}$是$M$中任意但不同的元素，证明$$\sum_{j=1}^{n} \frac{1}{x_{j}}<80$$