Simple fraction in lowest terms

Express the extended fraction at the right as a simple fraction in lowest terms.$\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{2}}}}$

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$\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{2}}}}$ = $\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{\dfrac{5}{2}}}}$ = $\dfrac{1}{2+\dfrac{1}{2+\dfrac{2}{5}}}$ = $\dfrac{1}{2+\dfrac{1}{\dfrac{12}{5}}}$ = $\dfrac{1}{2+\dfrac{5}{12}}$ = $\dfrac{1}{\dfrac{29}{12}}$ = $\dfrac{12}{29}$