[NOT HOMEWORK] I need some smart brains.

Sanji Himura

Sanji Himura

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United States
Azle, TX
supermanfromazle
SanjiHimura
A YouTuber by the name of Mathologer recently put out a video that disputes a video by Numberphile that said that +1+2+3+4...=-1/12. This video here (it is a bit of a watch, but worth it.)



In that video, around the 22-minute mark, he presents a unique problem that I have attempted to solve in the comments: +1+0-1+0+1+0-1+0...

My solution is as follows:

S= +1+0-1+0+1+0-1+0

Then I supersum the problem (explained in the video for those who don't know what Supersumming is)
S=1 1 0 0 1 1 0 0...

I supersum again and got this:
S=1 1 (2/3) (1/2) (3/5) (2/3) (4/7) (1/2)...

It is at this point where the series converges into a finite sum that I don't know what it is by two people, one is a random commenter and the other is by Mathologer himself. It is Mathologer who is currently provided me the biggest headache today when he asked to find other supersummable series by just moving the 0 around.

As someone who understands nothing of calculus, I would like to understand what I did and how the YouTuber was so impressed with my work.
 
According to both high school and a semester of college I somehow know some calculus, but I have no idea what's going on.
 
Oddly enough, I'm in my calculus class going over finite sums at this exact moment (break).

Definetly have to give this a watch.
 
Merely inferring the pattern of what you did, I guess the third series converges into (1/2). Not surprising if the second series just repeats two ones followed by two zeroes. After the first (1/2), the third series just alternates between three instances of 0.5 + (0.5 / n) and back to (1/2). But since (0.5 / n) approaches zero, you're left with (1/2).

I can't help you with "moving the 0 around", sorry.

I always did well in math up through pre-calculus, but the obsession with shorthand and the "meta" aspects of higher-level math are a brick wall to me.
 

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