# 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

$3 - \dfrac{2}{ 3 - \dfrac{2} { 3 - \dfrac{2} { 3 - \ddots } } }= \ ?$