# Proving It Is The Fun Part!

Algebra Level 5

$\dfrac1{(x+1)(x+2)\cdots(x+999) }$

The partial fraction decomposition of the expression above can be expressed as $$\displaystyle \sum_{m=1}^{999} \dfrac {a_m}{x+m}$$ for some $$a_1, a_2, \ldots , a_{999}$$.

If $$\max \{|a_1|, |a_2|, \ldots, |a_{999}|\} = \dfrac{1}{(Q!)^2}$$, find $$Q$$.

Notations:

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