An algebra problem by Hana Wehbi

Algebra Level 3

12!+23!+34!++99100!=11A!\frac{1}{2!} + \frac{2}{3!} + \frac{3}{4!} + \cdots + \frac{99}{100!} = 1 - \frac{1}{A!}

What is AA?

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

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