# 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, \(\gamma \approx 0.5772 \).