Showing posts with label supply sum method. Show all posts
Showing posts with label supply sum method. Show all posts

Tuesday, February 11, 2014

The sum of integers is -1/12 ... or not?

In the current days it seems that people picked up an old discussion and brought it to new attention in their forums. In heated debates they discuss and exchange their point of views, sometimes rather impolite than objective.

They talk about infinite sums of integers, in particular divergent sums, and show how these sums can be manipulated to be equal to a finite value. This causes trouble, since it seems on the first sight rather unintuitive and wrong.

The most used example for their offending object is the simple sum $$1 + 2 + 3 + 4 + ... = \sum^\infty_{i=1} i$$, which can be manipulated such that it is finally equal to $-1/12$. The first one who showed this curiosity was the famous mathematician Srinivasa Ramanujan. And from the fact that a credible mathematician wrote down those things, there should arise some doubt that maybe perhaps there is some truth in these formulas and that the misunderstandings come from the fact, that the formulas are probably not correctly cited and used.