Continued fraction question I have been given an continued fraction for a number x:
$$x = 1+\frac{1}{1+}\frac{1}{1+}\frac{1}{1+}\cdots$$
How can I show that $x = 1 + \frac{1}{x}$? I played around some with the first few convergents of this continued fraction, but I don't get close.

Just look at it.  OK, if you want something more proofy-looking: if $x_n$ is the $n$'th convergent, then $x_{n+1} = 1 + 1/x_n$.  Take limits.
