# A calculus problem by Hummus a

Calculus Level 5

$\large \displaystyle\lim _{ n\to\infty }{ \left( \dfrac { { a }_{ n }^{ \gamma } }{ { \gamma }^{ { a }_{ n } } } \right) ^{ 2n } }$

Let $${ a }_{ n }={ H }_{ n }-\ln { n }$$, where $${ H }_{ n }$$ denote the $$n^{\text{th}}$$ harmonic number.

If the limit above is equal to $$\dfrac { Ae }{ B\gamma }$$ for positive coprime integers $$A$$ and $$B$$, find $$A+B$$.

Notation: $$\gamma$$ denote the Euler-Mascheroni constant, $$\gamma \approx 0.5772$$.

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