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

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

#Algebra #Sharky

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
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Comments

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

Finn Hulse - 6 years, 12 months ago

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

Sharky Kesa - 6 years, 8 months ago

Oh shoot. Thanks for reminding me!

Finn Hulse - 6 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$