# Summation of a Series!

Algebra Level 5

$\large{ S = \sum_{k=1}^{2006} (-1)^k \dfrac{k^2 - 3}{(k+1)!}}$

If $$(S-1)$$ can be represented as $$\dfrac{A}{B!}$$ where $$A,B$$ are positive integers each less than 10,000, then find the value of $$A+B$$.

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