Terms of a Harmonic Progressions

Algebra Level 3

Let \(m\) and \(n\) be distinct positive integers such that

the \(m^\text{th} \) term of a harmonic progression is equal to \(n\);
the \(n^\text{th} \) term of the same harmonic progression is equal to \(m\).

Find the value of the \((mn)^\text{th} \) term of this progression.