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Find the sum of all real values of \(x\) that satisfy

 \(x = 1 - x + x^2 - x^3 + x^4 - x^5 + \dotsb.\)
 

 Jan 24, 2022
 #1
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By geometric series, 1 - x + x^2 - x^3 + ... = 1/(1 + x).

 

The equation is then x = 1/(x + 1).

Then x^2 + x - 1 = 0.

By Vieta's formulas, the sum of the roots is -1.

 Jan 24, 2022
 #2
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sorry, but... its wrong!

Guest Jan 24, 2022

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