1

So a couple of days ago I decided to learn why Ramanujan's theory 1+2+3+4+... = -1/12 is the way it is. The first step in the proof/derivation was to consider Grandi's series A = (1-1+1-1+1-1+1-1...) and how he "manipulated" it. The first thing he did was to consider 1-A and thus 1-(1-1+1-1+1-1...).

What I found strange is how he just fit an infinite series into parentheses. To me, that implies that the series is finite since in order to add the last bracket he would have to determine a last element of the series, or else he couldn't put a bracket there.

Is there a rule that I'm missing here or am I just completely missing the point of parentheses in maths in general?

Glace
  • 51
  • Excellent question. In the real numbers, this process is invalid for the exact reason you mention: putting it in parentheses implies that it has a finite value, which it doesn't. That being said, there are extensions to the reals numbers in which this process is defined. – Rushabh Mehta Nov 10 '21 at 22:15
  • Are you talking about complex numbers? I'm still pretty new to them but could you maybe go into more detail cause I'm quite curious. – Glace Nov 10 '21 at 23:07
  • No, even the complex numbers aren't sufficient. You need to "regularize" the real numbers, as done in this article – Rushabh Mehta Nov 10 '21 at 23:33

0 Answers0