I have a question concerning continued fractions:
If we have $\gamma \in \mathbb{R} \setminus \mathbb{Q}$ and $\gamma=\langle a_0;a_1,a_2,\dotsc\rangle$. Why do we get $\frac1\gamma = \langle 0;a_0,a_1,\dotsc\rangle$
Furthermore, how can I get the continued fraction of $\langle 0;\overline1 \rangle$?
Any help is appreciated.