Past exam of the options II for mathematics and philosophy course of the University of Oxford / 2013 / N2 / b / Solution

If $|s|\le 1$, then ${\sum }_k|p_k{s}^k|\le {\sum }_k{p}_k=1$. Thus the power series converges absolutely at every such real $s$, including both endpoints. ThereforeThe radius of convergence is at least one, though it can be larger for particular distributions.