# 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 $$\dfrac{2}{1-\alpha}+\dfrac{2}{1-\alpha^2}+\dfrac{2}{1-\alpha^3}+\cdots+\dfrac{2}{1-\alpha^n}$$?

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