E an EasyMethod!

Algebra Level 5

1+12α1+12α2+12α3++12αn1= ?\large 1+\dfrac{1}{2-\alpha_1}+\dfrac{1}{2-\alpha_2}+\dfrac{1}{2-\alpha_3}+\cdots +\dfrac{1}{2-\alpha_{n-1}}=~?

If 1,α1,α2,,αn11,\alpha_1,\alpha_2,\ldots, \alpha_{n-1} are nthn^{th} roots of unity, find the value of the above expression, taking n=9n=9.

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