1+2+3+…=-1/12, but not really

These people would have completely failed the calculus classes I took in undergrad. Why 1+2+3+…=-1/12.

To see why what they do is mathematical foolishness, see for example Riemann series theorem.

And interestingly enough there is some real math going on… See Ramanujan summation.

…which in no way implies the claim.

  1. It was obvious they weren’t talking about standard math when they said that the sum of the alternating series is 1/2. As for the “realness” some (including me) would claim that the whole idea of an infinite series is suspicious to say the least. It’s well known that even with the standard definitions, if you change the order of the numbers in the sequence you may get different results, which already diverges from our intuitive understanding of addition. Note that I’m not contesting in any way the importance of infinite series to math, or claim that the theory is useless.

    This reminds me of a joke: A mathematician, economist and biologist watch a man enter an empty building, and then two men come out. The biologist says: they procreated. The economist says: there was an interest of 100%. The mathematician says: If a man enters the building now, it would be empty again.


  2. Average limit of series