$$\frac{{{\pi ^2}}}{6} = \frac{3}{2} + \frac{1}{{7 - \frac{{{1^4}}}{{11 - \frac{{{2^4}}}{{19 - \frac{{...}}{{... - \frac{{{n^4}}}{{2{n^2} - 2n + 7 - ...}}}}}}}}}}$$