As easy as exponents

Calculus Level 3

A=n=01n!B=limnnn!nC=limn(1+1n)nD=1+1112233344\large\begin{aligned}A&=&\displaystyle\sum_{n=0}^{\infty}\dfrac{1}{n!}\\B&=&\displaystyle\lim_{n\to\infty}\dfrac{n}{\sqrt[n]{n!}}\\C&=&\displaystyle\lim_{n\to\infty}\left(1+\dfrac{1}{n}\right)^n\\D&=&1+\dfrac{1}{1-\dfrac{1}{2-\dfrac{2}{3-\dfrac{3}{3-\dfrac{4}{4-\cdots}}}}}\end{aligned}

Which option(s) has to be equals to ee?

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