Explanation of Feynman’s paradox concerning low-pass filters

In Feynman’s lectures there is a remark about the limiting value of the impedance of an n-section ladder consisting of purely reactive elements (capacitances and inductances). The remark is that the limiting impedance z = limn→∞ zn has a positive real part. He notes that this is surprising since the real part of each zn is zero, therefore it is impossible for the limit to have a positive real part. We explain the paradox, give the rate of convergence of the infinite sequence zn, calculate the speed at which energy is propagated out into the infinite ladder, and comment on some of the literature on this topic.