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

  1. 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.
     
  2. jcsd
  3. pwsnafu

    pwsnafu 909
    Science Advisor

    We had a recent thread on this.

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