# Interesting Sum of Unity

**Algebra**Level 5

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 \(\dfrac{2}{1-\alpha}+\dfrac{2}{1-\alpha^2}+\dfrac{2}{1-\alpha^3}+\cdots+\dfrac{2}{1-\alpha^n}\)?