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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\(\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{2}}}}\) = \(\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{\dfrac{5}{2}}}}\) = \(\dfrac{1}{2+\dfrac{1}{2+\dfrac{2}{5}}}\) = \(\dfrac{1}{2+\dfrac{1}{\dfrac{12}{5}}}\) = \(\dfrac{1}{2+\dfrac{5}{12}}\) = \(\dfrac{1}{\dfrac{29}{12}}\) = \(\dfrac{12}{29}\)