# 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.

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