# E an EasyMethod!

Algebra Level 5

$\large 1+\dfrac{1}{2-\alpha_1}+\dfrac{1}{2-\alpha_2}+\dfrac{1}{2-\alpha_3}+\cdots +\dfrac{1}{2-\alpha_{n-1}}=~?$

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

×