$${\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}$$ = $${\frac{{\mathtt{12}}}{{\mathtt{24}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{8}}}{{\mathtt{24}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{3}}}{{\mathtt{24}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}$$ = $${\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{23}}}{{\mathtt{24}}}}$$ = $$1\frac{23}{24}$$
$${\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}} = {\frac{{\mathtt{47}}}{{\mathtt{24}}}} = {\mathtt{1.958\: \!333\: \!333\: \!333\: \!333\: \!3}}$$
= $$1.958\overline3$$
Gruß radix
!