1+2+3+4+5.... = -1/12

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Re: 1+2+3+4+5.... = -1/12

#41  Postby archibald » Dec 01, 2016 12:37 pm

archibald wrote:
Cito di Pense wrote:Then there are multiple easy solutions to find, and you can get busy finding the next one.

-2?

That would seem to cover any number of fisherwomen.


Beyond that, I can't think how to find other (positive number) solutions?

I am open to being really impressed by anyone who can, especially if they have a method other than trial and error.
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Re: 1+2+3+4+5.... = -1/12

#42  Postby newolder » Dec 01, 2016 1:04 pm

archibald wrote:
newolder wrote:
archibald wrote:
newolder wrote:No. As shown at the wiki page, a new series is created from the partial sums that goes like:
1/1, 1/2, 2/3, 2/4, ... and the limit of this series is 1/2. This is then defined as the Cesaro sum of G.


Not following.

I didn't understand the 1st video, I don't speak french. But the second video starts with the summation of the G series (1-1+1-1+1-1+1...) as 0.5, which seems to me bogus, so the next steps don't matter.

The wiki page makes it clear. The 'swindle' is what you see so far. The solution is to take the limit of the series of partial sums means (oops!) and define that as the Cesaro sum of G. The series of partial sums means is called tn at the wiki. I cannot make it any clearer. Sorry.


So...the limit of all the means of the partial sums of the series tends towards 0.5 as we approach infinity. Is that it?

Now you've got the Cesaro sum. :thumbup: The next 'layer' takes the averages of the averages but there's no example series shown for this in the Mathlogger tube.
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Re: 1+2+3+4+5.... = -1/12

#43  Postby tuco » Dec 01, 2016 6:18 pm

Galactor wrote:
tuco wrote:
Galactor wrote:It's a bit of a groan this one. The infinite series of -1 +1 -1 +1 ... converging to 1/2 is deeply dissatisfying. Or whatever it was ...


Indeed, about as satisfying as square root of negative one :) as mentioned in one of the vids or perhaps even the three fisherwomen.


Or as mentioned in my post four posts earlier to your post. :mrgreen:


lol yeah I got to that one after I posted mine. Was hoping it would hmm not get mentioned. I even think I understand your reasoning and question about application. The thing is that maybe we dunno application yet so that's to me not too satisfying either.
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Re: 1+2+3+4+5.... = -1/12

#44  Postby archibald » Dec 01, 2016 10:12 pm

newolder wrote:
Now you've got the Cesaro sum. :thumbup: The next 'layer' takes the averages of the averages but there's no example series shown for this in the Mathlogger tube.


Thanks for your patience.
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Re: 1+2+3+4+5.... = -1/12

#45  Postby LjSpike » Dec 08, 2016 9:01 pm

I only watched a small bit of the video, but from an idiots perspective, the series of 1,-1,1,-1... would average to 0? (unless you wished to presume infinities to be not equal, but it'd still be infinitely close to 0).
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Re: 1+2+3+4+5.... = -1/12

#46  Postby tuco » Dec 08, 2016 9:22 pm

Well, idiot .. not a mathematical gangster perhaps :)
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Re: 1+2+3+4+5.... = -1/12

#47  Postby crank » Dec 08, 2016 9:44 pm

Would a 'trigger man' count as a mathematical gangster?
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Re: 1+2+3+4+5.... = -1/12

#48  Postby Sityl » Dec 09, 2016 5:51 am

I've seen this before. I know that it's just an issue of my not being able to understand it.

So three questions:

If 1+2 = 3, how can adding more positive integers cause a lower number?
If ... indicates an infinte series, how is the answer not infinity?
Does this result provide any insight into the nature of our universe?
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Re: 1+2+3+4+5.... = -1/12

#49  Postby LjSpike » Dec 09, 2016 1:48 pm

I'd have to side with Sityl. We'll just sit outside of this Mathfia logic for a while perhaps?
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Re: 1+2+3+4+5.... = -1/12

#50  Postby newolder » Dec 09, 2016 1:58 pm

Sityl wrote:I've seen this before. I know that it's just an issue of my not being able to understand it.

So three questions:

If 1+2 = 3, how can adding more positive integers cause a lower number?
If ... indicates an infinte series, how is the answer not infinity?
Does this result provide any insight into the nature of our universe?

The Mathlogger video (3rd video, post #2) covers most of this if you watch to the end but, basically, 1 It usually can't. 2 It usually is. 3 Any 'insight' is related to the methods and results obtained from the Riemann zeta function extended (analytically continued) to work at zeta = -1. The zeta function seems to be connected (by hypothesis) to the distribution of prime numbers.
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