# Who's up to the challenge? 34

Calculus Level 5

$\lim _{ n\to \infty } \left [ { \sqrt [ n+1 ]{ \Gamma (1)\Gamma \left( \frac { 1 }{ 2 } \right) \Gamma \left( \frac { 1 }{ 3 } \right) \cdots\Gamma \left( \frac { 1 }{ n+1 } \right) } \\ \quad \quad \quad \quad \quad \quad \quad -\sqrt [ n ]{ \Gamma (1)\Gamma \left( \frac { 1 }{ 2 } \right) \Gamma \left( \frac { 1 }{ 3 } \right) \cdots\Gamma \left( \frac { 1 }{ n } \right) } } \right ]$

If the limit above is equal to $$\dfrac {A}{e^B}$$, where $$A$$ and $$B$$ are positive integers, find $$A+B$$.

Notation: $$\Gamma(\cdot)$$ denotes the Gamma function.

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