1,2,3....9 Wait, where is 10?

Algebra Level 5

If \(f(x)\) is a least degree polynomial such that \(f(r)=\dfrac{1}{r}\) for \( r=1,2,3,\ldots,9\), compute \(f(10)\).

If your answer can be represented as \(\dfrac{m}{n}\), where \(m\) and \(n\) are coprime positive integers, find \(m+n\).