Posted: 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.
The next 'layer' takes the averages of the averages but there's no example series shown for this in the Mathlogger tube.