In the realm, where the sum of natural numbers is $-1/12$ :
$1+2+3+4+...=-1/12$
Is this true?:
$2+4+6+8+...=2*(1+2+3+4+...)=-2/12$
Can this kind of naive calculations always be done? -or are there dangers lurking in the infinity?
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I blame Numberphile and Phil Plait (Bad Astronomy) for this. This divergent series has been getting asked about here a few times a week for the past couple months... – colormegone Mar 19 '14 at 02:49
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http://www.imdb.com/title/tt1840309/ – Will Jagy Mar 19 '14 at 02:58