$$\begin{array}{l} \frac{1}{2} + \frac{2}{{1 + 2 \cdot \left( {\frac{1}{4} + \frac{4}{{1 + 4 \cdot \left( {\frac{1}{6} + \frac{6}{{1 + 6 \cdot \left( {...} \right)}}} \right)}}} \right)}} = \frac{{{\pi ^2}}}{8} - 1 + G, \hfill \\ {\text{где }}G{\text{ - постоянная Каталана}}{\text{.}} \hfill \\ \end{array} $$