Many cube roots

Calculus Level pending

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

\[ x_n = \sqrt[3]{x_{n-1} x_{n-2}x_{n-3}} \]

for \(n > 2\).

If \(x_0 = 1\), \(x_1 = 1\) and \(x_2 =10000\) what is

\[\large \lim_{n \to \infty} x_n?\]

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