How to find the terms of the continued fraction representation for $e^\pi$ The question is  -  Find the first ten terms of the continued fraction representation for $e^ \pi $

Algorithm:
Set $r_0$ to be your desired real number, in this case $\displaystyle e^\pi$.
Now, for $i=0,1,2,3,\ldots$, do the following steps:
Set $c_i=\lfloor r_i\rfloor$. This is the floor function.
Set $r_{i+1}=\frac{1}{r_i-c_i}$.
Your desired continued fraction is now $[c_0;c_1,c_2,c_3,\ldots]$.  
