can be obtained by typing
\cfrac{1}{\sqrt{2}+
\cfrac{1}{\sqrt{2}+
\cfrac{1}{\sqrt{2}+\dotsb
}}}
This produces better-looking results than straightforward use of frac.
Left or right placement of any of the numerators is accomplished by using
cfrac|[l]| or cfrac|[r]| instead of cfrac.