Continuing With Continued Fractions

Calculus Level 2

1=321=32321=3232321= \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

3232323= ? 3 - \dfrac{2}{ 3 - \dfrac{2} { 3 - \dfrac{2} { 3 - \ddots } } }= \ ?


Inspiration, see solution comments

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