Percent-ages

Algebra Level 3

1% of 2% of 3%  97% of 98% of 99% of 100 is equal to x!xx11\% \ \text{of} \ 2\% \ \text{of} \ 3\% \ \cdots \ 97\% \ \text{of} \ 98\% \ \text{of} \ 99\% \ \text{of} \ 100 \text{ is equal to } \dfrac{x!}{x^{x-1}}

What is the value of xx?

Notation: !! denotes the factorial notation. For example, 8!=1×2×3××88! = 1\times2\times3\times\cdots\times8 .

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