Question Number 100614 by bachamohamed last updated on 27/Jun/20
$$\:\:\underset{\boldsymbol{{k}}=\mathrm{0}} {\overset{\boldsymbol{{k}}=\boldsymbol{{n}}−\mathrm{1}} {\sum}}\frac{\boldsymbol{{ln}}\left(\boldsymbol{{k}}!\right)}{\mathrm{2}^{\boldsymbol{{k}}+\mathrm{1}} }\:=?\:\:\:\: \\ $$$$\:\:\boldsymbol{\mathrm{A}{ny}}\:\boldsymbol{{help}}\:? \\ $$