What could be an intuitive explanation for $\displaystyle \sum_{k=1}^{\infty}{\frac1{k\,2^k}} = \log 2$ ?
$\displaystyle \sum_{k=1}^{\infty}{\frac{1}{2^k}} = 1$ has a simple intuitive explanation with taking a unit distance and adding the successive halfs consecutively, is there a similar explanation for $\ln 2$?