Find the sum of all real values of \(x\) that satisfy
\(x = 1 - x + x^2 - x^3 + x^4 - x^5 + \dotsb.\)
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.
sorry, but... its wrong!