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