I think it would be helpful to explicitly write out the what you're calculating mathematically, e.g. \sum{k=1}^{\infty} (\frac{2^k}{k})*P[halting~by~step~k] = \sum{k=1}^{infty} (\frac{2^k}{k})(2^k) = \sum_{k=1}^{infty} \frac{1}{k} just to make it clear that this is the harmonic series. I know it's described in English, but the math is often helpful. (For posting latex, see also: http://lwlatex.appspot.com/. I don't know if that's the most up-to-date method, but it works.)