There are various summation methods, like Able, Borel, and Cesaro. There's also analytic continuation. On Wed, Apr 16, 2014 at 12:10 PM, Bernie Cosell <bernie@fantasyfarm.com> wrote:
I'm wondering what the solid [??] mathematical basis is for sum(n) = -1/12. I was looking at the series (which seems to be a starting place for the "proof" of -1/12) 1 - 1 + 1 - 1 .. and it can have any of a bunch of values, depending on how you look at it. {I vaguely recall from high school that you can sum it as (1-1) + (1-1) + (1-1), and so get the sum as being zero. OR you can sum it as 1 - (1 - 1) - (1 - 1) and get a sum as being 1. OR you can do the standard summation trick: S = 1 - 1 + 1 - 1 + 1 = 1 - S, ==> S = 1/2 and you can probably get it to "sum" to other values with other manipulations.
Are there some kind of [non algebraic?] extensions/definitions of 'sum' that are generally accepted for determining the "sums" of series that would appear not to have one.
/Bernie\
-- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--
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