What is up with people thinking that 1 + 2 + 3 + = -1/12?

[Jamin2112]

What is up with people thinking that 1 + 2 + 3 + ... = -1/12?

My friend showed me a Youtube video where a Physicist "proves" that ∑_kεNk = -1/12. The guy in the video uses a lot of illegal maneuvers. But apparently this "fact" is used in String Theory. Do Physicists use different definitions of convergence or something? I can easily prove that the sequence {1 + 2 + ... + n} is unbounded using the definitions I learned in Intro to Real Analysis in college.

 

[pwsnafu]

We had a recent thread on this.

tl;dr The manipulations are indeed invalid. But physicists do use the Zeta regularization in their work.