The "Unicode Nearly Plain-Text Encoding of Mathematics" standard[0] can do this just fine. :)

a_0+1/(a_1+1/(a_2+1/(⋱+(1/a_n ) )))

Past that into an editor that accepts the spec, and you'll get something like http://imgur.com/a/7hBwv

Disclaimer: I work @Microsoft improving on some math features, and we are the main implementors of the spec. Which makes me sad, since it is an open spec and it is really powerful!

[0]http://unicode.org/notes/tn28/UTN28-PlainTextMath-v3.pdf

PDF and OOXML are also open specifications.

Try to implement them though, you will run into a lot of issues.

I'm curious about that one - was the space necessary?

I just tried it out in Word, apparently it isn't. :)

Subscript and superscript are the bigger problem than fractions, also larger-than-one-line parentheses. Fractions can be aped in the ugly approach of dashes just like how Markdown underlines headers.

Matricial data is quite hard to explain well in a non-graphical mode, though.