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Sum of an integral

Calculus Level 3

$\large \sum_{n=1}^\infty \int_n^{n+1}xe^{-x}dx = \ ?$

Notation: $e \approx 2.718$ denotes the Euler's number.

\frac 6e

\frac 2e

\frac 8e

\frac 4e

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by Angel Loquez

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