# Back from a short holiday!

Calculus Level 5

$\large \sum _{ n=1 }^{ \infty }{ \dfrac { n{ H }_{ n } }{ { 2 }^{ n-1 } } } =A+\ln B$

The above equation holds true for positive integers $$A$$ and $$B$$. Find $$A+B$$.

Notation: $$H_n$$ denotes the $$n^\text{th}$$ harmonic number, $$H_n = 1 + \dfrac12 + \dfrac13 + \cdots + \dfrac1n$$.

Inspired by my own problem.

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