# Sum of Gaps

Calculus Level 2

Given that $$\displaystyle e = \sum_{k=0}^\infty \dfrac1{k!} \approx 2.718,$$ what is the value of $\displaystyle \sum_{n=0}^{\infty}\left(e- \sum_{k=0}^{n} \frac{1}{k!}\right) ?$

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