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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