\(2+\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{2}}}}=2+\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{\dfrac{5}{2}}}}\)
\(=2+\dfrac{1}{2+\dfrac{1}{2+\dfrac{2}{5}}}=2+\dfrac{1}{2+\dfrac{1}{\dfrac{12}{5}}}=2+\dfrac{1}{2+\dfrac{5}{12}}\)
\(=2+\dfrac{1}{\dfrac{29}{12}}=2+\dfrac{12}{29}=\dfrac{70}{29}\)
