Fearsome Factorials!

Algebra Level 3

If the value of

\(\sum^{2014}_{k =1} \frac{k}{(k + 1)!}\)

can be written in the form of

\(A + (-1)^{B} \cdot \frac{1}{C!}\), when \(A, B\) and \(C\) are postive integers and \(B\) is either \(1\) or \(2\),

find the value of \(A + B + C\).

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