Leaps and bounds

Calculus Level 3

Let \(x_n\) be a positive root of the equation \(x^n = x^2 + x + 1.\)

Find \(\displaystyle \exp\Big(\lim_{n \to \infty} n\left(x_n - 1\right)\Big).\)

\(\)
Notation: \(\exp( a ) = e^a\)

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