SUM FUN

Algebra Level 4

A very interesting problem from one of my Math Worksheets:

\[\displaystyle\sum_{k=1}^{2014} \dfrac{(k-1)k!}{2^k}\]

equals to \(\frac{a!}{b^c}-1\) for positive integers \(a,b,c\). Find the value of \(a+b+c\).

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