[passer-by]

29. Compute

$$ \sum_{n=1}^{\infty} \frac{1}{n \cdot 2^n}\bigg( 1+\frac{1}{2}+\cdots \frac{1}{n} \bigg) $$

HINT

The following might help
$$ \int_0^x \frac{-\ln(1-t)}{1-t} \,\, dt$$