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Algebra Level 5

\[\large \displaystyle \sum _{k=1}^{10}\dfrac{w^k}{2-w^k}\]

Let \(w=e^{2i\pi/10}\). If the value of the summation above is equal to \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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