Percent-ages

Algebra Level 3

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

What is the value of $x$ ?

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

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