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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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?
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:
newolder wrote:
Now you've got the Cesaro sum. The next 'layer' takes the averages of the averages but there's no example series shown for this in the Mathlogger tube.
Stephen Colbert wrote:Now, like all great theologies, Bill [O'Reilly]'s can be boiled down to one sentence - 'There must be a god, because I don't know how things work.'
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?
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