21st Century!

Algebra Level 4

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

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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