# Seriesly! Sum problems these days.

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

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

Note by Sharky Kesa
4 years, 3 months ago

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The key are the RoU. One you do that, it's super simple. More later.

- 4 years, 3 months ago

Later? Finn, you have some unfinished work. :P

- 3 years, 11 months ago

Oh shoot. Thanks for reminding me!

- 3 years, 11 months ago