Telescoping Problem

12015!+k=12014k(k+1)!=?\large \dfrac1{2015!} + \sum_{k=1}^{2014} \dfrac k{(k+1)!} = \, ?

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


Source: Indonesian Mathematic Olympiad 2014.
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