Leaps and bounds

Calculus Level 3

Let xnx_n be a positive root of the equation xn=x2+x+1.x^n = x^2 + x + 1.

Find exp(limnn(xn1)).\displaystyle \exp\Big(\lim_{n \to \infty} n\left(x_n - 1\right)\Big).


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

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