$$\text{Displayed nested fractions are normal size at the first level, }{\displaystyle \frac{1^{\sqrt{6}}}{\sqrt{2}+\frac{1}{\sqrt{3}+\frac{1}{\sqrt{4}+\frac{1}{\sqrt{5}+\frac{1}{\sqrt{6}+\dots }}}}}}\text{ script size at second level, and script-script size at all more nested levels.}$$