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Posted on: February 7th, 2016 by
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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.

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