Summing reciprocal factorials

Algebra Level 3

Find the closed form of the sum r=1nr(r+1)! \displaystyle \sum_{r=1}^{n} \dfrac{r}{(r+1)!} .

Notation: !! denotes the factorial function. For example, 8!=1×2×3××88! = 1\times2\times3\times\cdots\times8 .

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