Geometrically sound

Algebra Level 4

\[\dfrac{3}{17}+\dfrac{33}{17^2}+\dfrac{333}{17^3}+ \dfrac{3333}{17^{4}}+\cdots \]

If the value of the series above is in the form \(\dfrac{m}{n}\), where \(m\) and \(n\) are coprime positive integers, find \(m+n\).

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