\[\frac{{{\pi ^2}}}{6} = \frac{1}{1} + \frac{{\frac{1}{2} + \frac{{\frac{1}{3} + \frac{{\frac{1}{4} + \frac{{\frac{1}{5} + ...}}{{\frac{5}{4}}}}}{{\frac{4}{3}}}}}{{\frac{3}{2}}}}}{{\frac{2}{1}}}.\]