Comments by "RB 70" (@RB-bd5tz) on "The Return of -1/12 - Numberphile" video.

I finally get it! This video explains better than the original from ten years ago that the sum of the natural numbers is -1/12 only if you violate rules ("analytic continuation") and carry out selective, arbitrary operations. 6:02 X = 1 + r + r^2 + r^3 + ... only equals a number if |r| < 1. Fine. 11:45 X = 1 + 10 + 100 + 1000 + ... = -1/9 only if you violate the rule that |r| < 1 (i.e., r = 10 (11:29)). Otherwise, it would obviously and correctly zoom to infinity. 17:30 X = 1 + 2 + 3 + 4 + ... = -1/12 only if you violate the rule that |r| < 1 (i.e., r = -1 (14:00)) AND arbitrarily select -4 as a factor and add terms in a very specific way (16:00); otherwise, you can get many different sums. Now I can rest easy, happily knowing that X = 1 + 2 + 3 + 4 + ... actually does go to infinity and that these results are bogus hocus-pocus.
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@nintendoswitchfan4953 I stand by my comment; they put invalid r values in a formula where the rule is |r|<0, and obtained nonsense, as expected; that's the reason for the rule. They also used arbitrary constants in calculations, with no justification, to help obtain the nonsense. It's patently obvious that if you add infinite positive numbers, you're on your way to positive infinity. The US national debt keeps going up; when will it reach -1/12?
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