Limits + Summation = Fun

Calculus Level 5

\[\large \lim _{ x\rightarrow \infty }{ \sum _{ n=1 }^{ x }{ \left\{ \frac { x }{ n } \right\} } =A-B\gamma } \]

The equation above holds true for positive integers \(A\) and \(B\). Find \(A+B\)

Notation: \(\{\cdot \}\) denotes the fractional part function.

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