\[ \large \displaystyle\lim _{ x\rightarrow \infty }{ \sum _{ n=1 }^{ x }{ \left( \Gamma \left(\dfrac { n }{ x } \right) \right) ^{ -n } } } =\dfrac { { e }^{ \gamma } }{ { e }^{ \gamma }-1 } \]

Prove that the equation above holds true.

**Note**: This is an open problem. Numerical computations show this to be its value. If you come up with a solution, I recommend publishing it and congrats if you do!

**Notations**:

\( \Gamma(\cdot) \) denotes the Gamma function.

\( \gamma\) denotes the Euler-Mascheroni constant, \(\gamma \approx 0.5772 \).

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