21st Century!

Algebra Level 4

2002 ! 2001 ! + 2000 ! + + 2 ! + 1 ! = ? \large \displaystyle \left \lfloor \frac{2002!}{2001! + 2000! + \cdots + 2! + 1!} \right \rfloor = \, ?

Notations :

  • ! ! denotes the factorial notation. For example, 8 ! = 1 × 2 × 3 × × 8 8! = 1\times2\times3\times\cdots\times8 .

  • \lfloor \cdot \rfloor denotes the floor function .


The answer is 2000.

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