水一个恒等式

Czhang271828

\begin{align*}
&3+\dfrac{3}{2}+\dfrac{9}{7}+\dfrac{81}{67}+\dfrac{6561}{5623}\\
=\,&3\times \dfrac{3}{2}+\dfrac{9}{7}+\dfrac{81}{67}+\dfrac{6561}{5623}\\
=\,&3\times\dfrac{3}{2}\times\dfrac{9}{7}+\dfrac{81}{67}+\dfrac{6561}{5623}\\
=\,&3\times\dfrac{3}{2}\times\dfrac{9}{7}\times\dfrac{81}{67}+\dfrac{6561}{5623}\\
=\,&3\times\dfrac{3}{2}\times\dfrac{9}{7}\times\dfrac{81}{67}\times\dfrac{6561}{5623}
\end{align*}

hbghlyj

\begin{align*}
a_1&=3\\
a_2&=3+\dfrac{3}{2}\\
a_3&=3+\dfrac{3}{2}+\dfrac{9}{7}\\
a_4&=3+\dfrac{3}{2}+\dfrac{9}{7}+\dfrac{81}{67}\\
a_5&=3+\dfrac{3}{2}+\dfrac{9}{7}+\dfrac{81}{67}+\dfrac{6561}{5623}\\
a_{n+1}&=\cfrac{a_n}{1-\cfrac{1}{a_n}}
\end{align*}
发现这里有Czhang271828的签名档“呾什物，我亲像，古早亓西施”的台罗注音:

1. 講啥物我親像
2. kóng siánn-mih guá tshin-tshiūnn
3. 古早的西施
4. kóo-tsá ê Se-si

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