Ambiguity of some infinite math expressions

I've come to realize that I don't actually know precisely how to interpret some infinite math expressions with an ellipsis ("…"), like $latex \sqrt{1 + \sqrt{1 + \sqrt{1 + \dots} } }$ First, to flatten out the syntax, I'll define $latex R$ to be the square root function: $latex R(x) = \sqrt{x}$. Now evaluate the …