An algebra problem by Hana Nakkache

Algebra Level 3

\[\frac{1}{2!} + \frac{2}{3!} + \frac{3}{4!} + \cdots + \frac{99}{100!} = 1 - \frac{1}{A!}\]

What is \(A\)?

\(\) Notation: \(!\) is the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

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