USE OF PHYSICAL ANALOGS TO EVALUATE INFINITE SERIES

We consider two physical examples that lead to infinite series: (i) the Madelung energy of a one-dimensional array of alternating positive and negative charges and (ii) a point charge between infinite parallel plates. The series for the first example is conditionally convergent, and therefore, the sum is dependent upon term ordering. However, for each arrangement there exists a specific physical analog. The series of infinite images arising in the second example is divergent. Here, the physical analog is not helpful in evaluating the sum. We point out that failure of the analog is tied to certain historical difficulties encountered in the development of the theory of divergent series. © 1979, American Association of Physics Teachers. All rights reserved.