I just went upstairs and dug out my copy of Marsden's "Elementary Classical Analysis" (don't you love the way advanced maths books are "elementary this", or "elementary that" - except for my favourite, "Mathematics Made Difficult", by Linderholm).
It's the concept of Cesaro 1-summability that I was dimly recalling (page 125), but on page 126, it appears the same result is achieved by Abel summability, which is more general. Getting back to the sum of the integers - the Abel sum is the zeta function, and the analytic continuation of such is the value of -1/6 that's been quoted. It's one of those funny little topics taught in second year maths without any context, and which is almost immediately forgotten as useless. Cheers On Thu, Jan 30, 2014 at 10:57:21AM +1300, LizR wrote: > On 30 January 2014 10:28, Russell Standish <li...@hpcoders.com.au> wrote: > > > As someone pointed out, it requires a non-standard definition of > > convergence, as these series are non-convergent according to the usual > > Cauchy definition. > > > > Surely they are non convergent full stop? > > But even so I can't offhand see what's wrong with my son's proof that the > series sums to 1/2 (a couple of posts back). It doesn't seem to require > convergence...??? > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com. > To post to this group, send email to everything-list@googlegroups.com. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
