Explain this to a middle / high school student

Question

I have come across the proof that all natural numbers to infinity when summed equals -1 / 12 and can not quite grasp this. Could anyone find a way to explain this in an easy understandable way for someone still in school (for that one kid who says he gets this and he's still in school, good for you).

Here's the video I saw : https://www.youtube.com/watch?v=w-I6XTVZXww

Thanks!

Answer 1

I think that there is no ''easy understandable way'' to explain this result to a middle/high school student.

It is really a strange result because this series does not have a limit in the usual sense, and this value is found using a more general definition of the sum of a series and a method that use the properties of an analytic function (the zeta function regularization) so that the knowledge of the complex analysis is needed to understand the result.

There are different methods to define the ''sum'' of a divergent series and the reference book for this topic is G. Hardy, Divergent series.

You can see also other questions about this topic as: Is $1+2+3+4+\cdots=-\frac{1}{12}$ the unique ''value'' of this series?