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1992 OIM Problems/Problem 2

Revision as of 13:55, 13 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Given the collection of <math>n</math> positive real numbers <math>a_1 < a_2 < a_3 < \cdots < a_n</math> and the function: <cmath>f(x) = \frac{a_1}{x+a_1}+\frac...")
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Problem

Given the collection of $n$ positive real numbers $a_1 < a_2 < a_3 < \cdots < a_n$ and the function:

\[f(x) = \frac{a_1}{x+a_1}+\frac{a_2}{x+a_2}+\cdots +\frac{a_n}{x+a_n}\]

Determine the sum of the lengths of the intervals, disjoint two by two, formed by all $x = 1$.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe7.htm

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