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オリジナルの投稿元:Secular Sevens
2/11/2014 2:03:46 AM
20
1+2+3+4+... = -1/12
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Ryanにより編集済み: 2/11/2014 1:21:20 PMNote that that sum, in the conventional sense, doesn't converge. That series is clearly divergent, however, there are different ways to sum divergent series allowing you to "assign" values to a particular divergent series (e.g. Ramanujan summation, or Cesaro Summation). The original series still diverges to plus infinity though.
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3 通の返信BannedPiranhaにより編集済み: 2/11/2014 2:26:13 AMYes. The Flood has already gone over this. I'm still sort of amazed at the people that deny this result despite the proof and it's use in physics. Here's the alternate proof.
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3 通の返信This is the problem with concepts, they don't match up with reality perfectly. Hence, weirdness like this in maths and physics.
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2 通の返信Regretにより編集済み: 2/11/2014 5:52:49 PMI'm pretty sure that doesn't work. The sum of (-1)^(n-1) doesn't equal a half. You can't just take an average, it doesn't work like that.
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2 通の返信
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1 返信I'm never going to understand how adding an infinite number of positive integers will result in a negative answer. Maybe it's explained in the video, but I can't watch it at the moment
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1 返信I still don't understand how finding the average of something is the same as finding its sum.
