\begin{align} \mathrm e &= 2 + \cfrac{1}{1 + \cfrac{1}{2 + \cfrac{1}{1 + \cfrac{1}{1 + \cfrac{1}{4 + \cfrac{1}{1 + \cfrac{1}{1 + \cfrac{1}{6 + \cfrac{1}{1 + \cfrac{1}{1 + \cfrac{1}{8 + \cfrac{1}{\ddots}}}}}}}}}}}}\\ &=[2;1,2,1,1,4,1,1,6,1,1,8,\ldots] \end{align}