SUM FUN

Algebra Level 4

A very interesting problem from one of my Math Worksheets:

k=12014(k1)k!2k\displaystyle\sum_{k=1}^{2014} \dfrac{(k-1)k!}{2^k}

equals to a!bc1\frac{a!}{b^c}-1 for positive integers a,b,ca,b,c. Find the value of a+b+ca+b+c.

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