Question 2
Let $a,b,A,B$ be positive real numbers. Define $x_1=a$, $x_2=b$ and
$$x_{n+1}=A\sqrt[3]{x_n^2}+B\sqrt[3]{x_{n-1}^2}\qquad(n=2,3,4,\ldots).$$
Prove that $\lim_{n\to\infty}x_n$ exists and determine it.
$$x_{n+1}=A\sqrt[3]{x_n^2}+B\sqrt[3]{x_{n-1}^2}\qquad(n=2,3,4,\ldots).$$
Prove that $\lim_{n\to\infty}x_n$ exists and determine it.