$$1 + \cfrac{1}{{1 + \cfrac{2}{{1 + \cfrac{3}{{1 + \cfrac{4}{{1 + ...}}}}}}}} = \cfrac{2}{{1 + \cfrac{1}{{1 + \cfrac{4}{{1 + \cfrac{3}{{... + \cfrac{{2n}}{{1 + \cfrac{{2n - 1}}{{1 + ...}}}}}}}}}}}}$$