# A Simplified Explanation of What It Means to Assign a Finite Value to an Infinite Sum

## Publication Date

4-2015

Technical Report: UTEP-CS-15-34

To appear in Journal of Uncertain Systems, 2016, Vol. 10.

## Abstract

Recently, a video made rounds that explained that it often makes sense to assign finite values to infinite sums. For example, it makes sense to claim that the sum of all natural numbers is equal to -1/12. This has picked up interested in media. However, judged by the viewers' and readers' comments, for many viewers and readers, neither the video, not the corresponding articles seem to explain the meaning of the above inequality clearly enough. One of the main stumbling blocks is the fact that the infinite sum is clearly divergent, so a natural value of the infinite sum is infinity. What is the meaning of assigning a finite value to this (clearly infinite) sum? While the explanation of the above equality is difficult to describe in simple terms, the main idea behind this equality can be, in our opinion, explained rather naturally, and this is what we do in this paper.

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