# Many cube roots

Calculus Level 4

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

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

×