\(\dfrac{4\times{3}\times{2}\times{1}}{3!+2!+1!}\)+\(\dfrac{5\times{4}\times{3}\times{2}}{4!+3!+2!}\)+.......+\(\dfrac{2015\times{2014}\times{2013}\times{2012}}{2014!+2013!+2012!}\)= \(a\)

Find \(\lfloor{a}\rfloor\)

\(\lfloor...\rfloor\) is the greatest integer less than equal to [\(...\)]

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