Just to clarify, the above is not "my" equation. It is something that mathematicians (not me) figured out, repeatedly, many times over. Of course, the -1/12 nu

Just to clarify, the above is not "my" equation. It is something that mathematicians (not me) figured out, repeatedly, many times over. Of course, the -1/12 number is preposterous, but it does turn out to have a physical meaning. There are many ways of making the sum, including limit of partial-sums/summation by parts (the one we use most of the time), but there is also Abel summation, Borel summation, Ramanujan, Cesaro, and more. And frankly there is no reason to think that "summation by parts" is the "right" way. It is surely not "right" in physics. Example: why do we start summation from 1? Is the first element somehow more important than others? No, that is just our (ie human) arbitrary pick.