As easy as exponents

Calculus Level 3

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

Which option(s) has to be equals to \(e\)?

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