MathDB

Given the positive real numbers

a_{1}<a_{2}<\cdots<a_{n}

, consider 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 disjoint intervals formed by all the values of

x

such that

f(x)>1

Problem Statement