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Given that e=∑k=0∞1k!≈2.718,\displaystyle e = \sum_{k=0}^\infty \dfrac1{k!} \approx 2.718, e=k=0∑∞k!1≈2.718, what is the value of ∑n=0∞(e−∑k=0n1k!)? \displaystyle \sum_{n=0}^{\infty}\left(e- \sum_{k=0}^{n} \frac{1}{k!}\right) ?n=0∑∞(e−k=0∑nk!1)?
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