Example 1. Find $\frac{1}{1-\frac{1}{1-\cdots \frac{1}{1-\frac{355}{113}}}}$.
Let $a_{-}=\underbrace{-\frac{1}{1-\frac{1}{1-\cdots \frac{1}{1-\frac{355}{113}}}}}_{m}$.
$a_{1}=\frac{1}{1-\frac{355}{113}}=-\frac{113}{242}, a_{2}=\frac{244}{355}, a_{3}=\frac{355}{113}$,
$a_{4}=-\frac{113}{242}, a_{5}=\frac{242}{355}, \cdots$. From this, it is easy to see that $\left\{a_{n}\right\}$ is a periodic sequence with a period of 3. Since $1995=3 \times 665$. Therefore, the required value is $\frac{355}{113}$.