Publication Date



Technical Report: UTEP-CS-18-56


Infinities are usually an interesting topic for students, especially when they lead to what seems like paradoxes, when we have two different seemingly correct answers to the same question. One of such cases is summation of divergent infinite sums: on the one hand, the sum is clearly infinite, on the other hand, reasonable ideas lead to a finite value for this same sum. A usual way to come up with a finite sum for a divergent infinite series is to find a 1-parametric family of series that includes the given series for a specific value p = p0 of the corresponding parameter and for which the sum converges for some other values p. For the values p for which this sum converges, we find the expression s(p) for the resulting sum, and then we use the value s(p0) as the desired sum of the divergent infinite series. To what extent is the result reasonable depends on how reasonable is the corresponding generalizing family. In this paper, we show that from the physical viewpoint, the existing selection of the families is very natural: it is in perfect accordance with the natural symmetries.