We consider the convergence of the random harmonic series $latex \displaystyle R = \sum_{n=1}^{\infty}\frac{\sigma_{n}}{n} &fg=000000$ where $latex {\sigma_n\in\{-1,+1\}}&fg=000000$ is chosen randomly with probability $latex {1/2}&fg=000000$ of being either plus one or minus one. It follows from the Kolmogorov three-series theorem that the series is ``almost surely'' convergent. We are all familiar with the harmonic series … Continue reading Random Harmonic Series →