Interesting Sum of Unity

Algebra Level 4

The polynomial \(P(z) \equiv z^{n+1}-1\) has roots \(1,\alpha,\alpha^2 \ldots ,\alpha^n\), where \(\alpha\) is a complex \((n+1)^{\text{th}}\) root of unity.

What is the value of \(\dfrac{2}{1-\alpha}+\dfrac{2}{1-\alpha^2}+\dfrac{2}{1-\alpha^3}+\cdots+\dfrac{2}{1-\alpha^n}\)?

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