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1+12−α1+12−α2+12−α3+⋯+12−αn−1= ?\large 1+\dfrac{1}{2-\alpha_1}+\dfrac{1}{2-\alpha_2}+\dfrac{1}{2-\alpha_3}+\cdots +\dfrac{1}{2-\alpha_{n-1}}=~?1+2−α11+2−α21+2−α31+⋯+2−αn−11= ?
If 1,α1,α2,…,αn−11,\alpha_1,\alpha_2,\ldots, \alpha_{n-1}1,α1,α2,…,αn−1 are nthn^{th}nth roots of unity, find the value of the above expression, taking n=9n=9n=9.
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