# Recurring Styles #14 - Nested Radicals!

Calculus Level 5

$\large{ x_{n+1} = \sqrt{2+x_n} \quad, \quad x_1 = \sqrt{2} }$

Consider the sequence $$(x_n)_{n \in \mathbb Z^+}$$ as defined above. Let $$L = \displaystyle \lim_{n \to \infty} 4^n(2-x_n)$$. If $$L$$ can be expressed in the form $$\dfrac{A}{B} \pi^C$$ for positive integers $$A,B,C$$, find the minimum value of $$A+B+C$$.

Bonus: Generalize $$x_n$$ in terms of $$n$$.

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