$$1 + \cfrac{{1 + \cfrac{{1 + \cfrac{{1 + \cfrac{{1 + ...}}{{4s + 1}}}}{{3s + 1}}}}{{2s + 1}}}}{{s + 1}} + \cfrac{1}{{\cfrac{s}{{1 + \cfrac{{s - 1}}{{1 + \cfrac{{2s}}{{1 + \cfrac{{2s - 1}}{{1 + \cfrac{{3s}}{{1 + \cfrac{{3s - 1}}{{1 + ...}}}}}}}}}}}}}} = {s^{\frac{1}{s} - 1}}{e^{\frac{1}{s}}}\Gamma \left( {\frac{1}{s}} \right)$$ \[s > 0,{\text{ }}s \ne \frac{1}{n};\]