# 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 $$m+n$$.

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