# Calculus 4 - by Vlad Vasilescu (W)

Calculus Level 4

Let $$f(x)=\dfrac{1}{1+x}$$ and $$\displaystyle a_{n}= \sum_{k=0}^n \frac{(-1)^k}{k!}f^{(k)}(1)$$, where $$f^{(k)}(x)$$ is the $$k^{th}$$ derivative of $$f(x)$$.

Find $$\displaystyle \lim_{n\to \infty} a_{n}$$ .

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