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Let $ 1, \omega_2, \omega_3, \omega_4\cdots \omega_n$ be the roots of the equation$$ x^n=1,$$ then find the value of

$$\frac{1}{2-\omega_2} + \frac{1}{2-\omega_3}+ \frac{1}{2-\omega_4} + \cdots+ \frac{1}{2-\omega_n}$$ In terms of $ n$.

I tried many ways but was not able to solve this. If you see this message, then your question was automatically blocked by the server. All new questions are subjected to a "minimum quality" filter that checks for some basic indicators of a good, complete question. Check to make sure that your question has the following:

IrbidMath
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    Since you said you tried many ways to solve it , would you mind sharing with us those ways and thoughts on this problem ? – The Demonix _ Hermit Nov 29 '19 at 12:08
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    See https://math.stackexchange.com/questions/2209034/finding-sum-k-0n-1-frac-alpha-k2-alpha-k-where-alpha-k-are-the OR https://math.stackexchange.com/questions/1909362/product-of-one-minus-the-tenth-roots-of-unity – lab bhattacharjee Nov 29 '19 at 12:12
  • The $\omega_i$ are roots of a polynomial of degree $n$. Can you find a polynomial of degree $n$ whose roots are $1/(2-\omega_i)$? – almagest Dec 02 '19 at 09:48

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