# Continuing With Continued Fractions

**Calculus**Level 2

\[ \begin{array} {l l}
1 & = 3 - \frac{2}{1} \\
& = 3 - \frac{2}{ 3 - \frac{2}{1} } \\

& = 3 - \frac{2}{ 3 - \frac{2} { 3 - \frac{2}{1} } } \\

& = \ldots \\
\end{array}
\]

Observe the construction of the continued fraction above.

What is the value of

\[ 3 - \dfrac{2}{ 3 - \dfrac{2} { 3 - \dfrac{2} { 3 - \ddots } } }= \ ? \]