L'Hopital is Invalid!

Calculus Level 3

\[\large\ \lim _{ n\rightarrow \infty }{ \frac { e{ \left( 1 - \frac { 1 }{ n } \right) }^{ n } - 1 }{ { n }^{ \alpha } } } \]

If the limit above exists and is equal to a non-zero constant \(c\), then find the value of \(12(c - \alpha)\).

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