Nth number of continued fraction Given a real number $r$ and a non-negative integer $n$, is there a way to accurately find the $n^{th}$ (with the integer being the $0^{th}$ number in the continued fraction. If this can not be done for all $r$ what are some specific ones, like $\pi$ or $e$. I already now how to do this square roots.

You can do it recursively: $$\eqalign{f_0(r) &= \lfloor r \rfloor\cr
f_{n+1}(r) &= f_n\left( \frac{1}{r - \lfloor r \rfloor}\right)\cr}$$
Of course this may require numerical calculations with very high precision.
Actually, if $r$ is a rational number but you don't know it, no finite precision
numerical calculation will suffice. 
