Some Harmonic sum

Calculus Level 5

\[\displaystyle \large \sum_{n=1}^{\infty}\dfrac{H_{n}}{2^{n+1} (n+1)} = ?\]

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

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