$\large \displaystyle \left \lfloor \frac{2002!}{2001! + 2000! + \cdots + 2! + 1!} \right \rfloor = \, ?$
Notations :
$!$ denotes the factorial notation. For example, $8! = 1\times2\times3\times\cdots\times8$ .
$\lfloor \cdot \rfloor$ denotes the floor function .
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