## 1988

Posted on: February 7th, 2016 by

Consider the inequality

$\frac{1}{x-1} + \frac{2}{x-2} + \frac{3}{x-3} + \dots \frac{70}{x-70} \geq \frac{5}{4},$
where $x$ is real.
Show that the sum of the lengths of the disjoint intervals that satisfy the above inequality is 1988.

- via International Math Olympiad 1988.