回復 50# mathca 的帖子
應該是這樣
\(\begin{align}
& {{x}_{n+1}}+{{y}_{n+1}}\sqrt{3}={{\left( 2+\sqrt{3} \right)}^{n+1}}=\left( {{x}_{n}}+{{y}_{n}}\sqrt{3} \right)\left( 2+\sqrt{3} \right)=\left[ \left( 2{{x}_{n}}+3{{y}_{n}} \right)+\left( {{x}_{n}}+2{{y}_{n}} \right)\sqrt{3} \right] \\
& \frac{{{x}_{n+1}}}{{{y}_{n+1}}}=\frac{2{{x}_{n}}+3{{y}_{n}}}{{{x}_{n}}+2{{y}_{n}}}=\frac{2\left( \frac{{{x}_{n}}}{{{y}_{n}}} \right)+3}{\left( \frac{{{x}_{n}}}{{{y}_{n}}} \right)+2} \\
\end{align}\)
