Non-stoppin' inspirations

Algebra Level 3

\[\large \dfrac{1}{2!}+\dfrac{2}{3!}+\dfrac{3}{4!}+\cdots +\dfrac{n-1}{n!} = \, ? \]

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

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