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Periodic continued fraction of a quadratic irrational

Continued fraction of the square root of eleven

If $p_n/q_n$ are the convergents of $\sqrt{11}$, then
$$
p_{n+1}+q_{n+1}\sqrt{11}
=\begin{cases}
(3+\sqrt{11})(p_n+q_n\sqrt{11}),&n\text{ odd},\\
\dfrac{3+\sqrt{11}}2(p_n+q_n\sqrt{11}),&n\text{ even}.
\end{cases}
$$


Alternating multiplier recurrence for convergents of the square root of eleven

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 4 / 1G / Solution

Alternating multiplier recurrence for convergents of the square root of eleven

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Alternating multiplier recurrence for convergents of the square root of eleven

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