No. For p coprime to 12, the p-adic norm of -1/12 is 1. But the partial sum n(n+1) has p-adic norm at most 1/p when n or n+1 is a multiple of p. -- Gene
________________________________ From: Mike Stay <metaweta@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Cc: Eugene Salamin <gene_salamin@yahoo.com> Sent: Friday, February 28, 2014 3:03 PM Subject: Re: [math-fun] Fwd: numberphile.com
On Fri, Feb 28, 2014 at 3:45 PM, Dan Asimov <dasimov@earthlink.net> wrote:
That I can agree with! (But the URL sent by Bob Baillie showed the equation 1+2+3+ . . . = -1/12 as a partial visual description of the video, something I can't agree with.)
Does that equation make sense p-adically for p coprime to 12? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com