Let \(x_1, x_2, \ldots, x_{n - 1}\), be the zeroes different from 1 of the polynomial \(P(x) = x^n -1, n \geq 2\).

Prove that

\[\frac {1}{1 - x_1} + \frac {1}{1 - x_2} + \ldots + \frac {1}{1 - x_{n - 1}} = \frac {n - 1}{2}.\]

Let \(x_1, x_2, \ldots, x_{n - 1}\), be the zeroes different from 1 of the polynomial \(P(x) = x^n -1, n \geq 2\).

Prove that

\[\frac {1}{1 - x_1} + \frac {1}{1 - x_2} + \ldots + \frac {1}{1 - x_{n - 1}} = \frac {n - 1}{2}.\]

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## Comments

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TopNewestThe key are the RoU. One you do that, it's super simple. More later. – Finn Hulse · 3 years, 1 month ago

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– Sharky Kesa · 2 years, 9 months ago

Later? Finn, you have some unfinished work. :PLog in to reply

– Finn Hulse · 2 years, 9 months ago

Oh shoot. Thanks for reminding me!Log in to reply