Evaluate the value of $$\lim_{n \to \infty}\frac{x_n}{\prod_{i=1}^{n-1} x_i}$$ where $x_n=x_{n-1}^2-2, (x_1=5).$
I've found that $x_n$ is an increasing sequence so that the limit becomes an indeterminate form of $(\frac{\infty}{\infty})$. I can't think of any other workable ideas though. Some hints are appreciated.