Find the limit of $2^n/x_n$ if $x_1=1$ and $ x_{n+1} = x_{n} + \sqrt{x_n^2 + 1}$ for every $n$

Question

Let $ x_1 = 1$ and $$ x_{n+1} = x_{n} + \sqrt{x_n^2 + 1}$$ Find the limit $$\lim_{n\to \infty} \frac{2^n}{x_n}$$

This is what I've found so far:

$$ x_{n+1} - 2x_n = \sqrt{x_n^2 + 1} - x_n = \frac{1}{\sqrt{x_n^2+1}+x_n} = \frac{1}{x_{n+1}}$$ How should I proceed?