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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