# All you're ever gonna be is "mean"

Calculus Level 4

Let $$x_0, x_1, x_2,\ldots$$ be a sequence of real numbers satisfying the recursion,

$x_n = \sqrt{x_{n-1} x_{n-2}}$

for $$n = 2,3,4,\ldots$$.

If $$x_0 = 1$$ and $$x_1 = 1000000$$, what is

$\large \lim_{n \to \infty} x_n ?$

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