Interesting Sum of Unity

Algebra Level 5

The polynomial P(z)zn+11P(z) \equiv z^{n+1}-1 has roots 1,α,α2,αn1,\alpha,\alpha^2 \ldots ,\alpha^n, where α\alpha is a complex (n+1)th(n+1)^{\text{th}} root of unity.

What is the value of 21α+21α2+21α3++21αn\dfrac{2}{1-\alpha}+\dfrac{2}{1-\alpha^2}+\dfrac{2}{1-\alpha^3}+\cdots+\dfrac{2}{1-\alpha^n}?

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