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Find the closed form of the sum ∑r=1nr(r+1)! \displaystyle \sum_{r=1}^{n} \dfrac{r}{(r+1)!} r=1∑n(r+1)!r.
Notation: !!! denotes the factorial function. For example, 8!=1×2×3×⋯×88! = 1\times2\times3\times\cdots\times8 8!=1×2×3×⋯×8.
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