Maximum value of a sum of square roots
Source: Romanian TST 2 2008, Problem 1
June 7, 2008
functioninequalities proposedinequalities
Problem Statement
Let be an odd integer. Determine the maximum value of
\sqrt{|x_{1}\minus{}x_{2}|}\plus{}\sqrt{|x_{2}\minus{}x_{3}|}\plus{}\ldots\plus{}\sqrt{|x_{n\minus{}1}\minus{}x_{n}|}\plus{}\sqrt{|x_{n}\minus{}x_{1}|},
where are positive real numbers from the interval .