# Triple Reciprocal Factorial Sum

Algebra Level 5

$\dfrac{3}{1! + 2! + 3!} + \dfrac{4}{2! + 3! + 4!} + ...... + \dfrac{2012}{2010! + 2011! + 2012!}$

If the above expression can be simplified to the form $$\dfrac{1}{a!} - \dfrac{1}{b!}$$ for positive integers $$a,b$$, what is the value of $$a+b$$?

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