\[\begin{array}{l} 1 + \frac{{1 + \frac{{1 + \frac{{...}}{{{a_3}}}}}{{{a_2}}}}}{{{a_1}}} = 1 + \frac{{\Gamma {{\left( {\frac{1}{4}} \right)}^2}}}{{4\sqrt {2\pi } }}, \hfill \\ {a_n} = 1 + \frac{{2n}}{{2n + 1}}. \hfill \\ \end{array} \]