-1/12 or: Why I stopped worrying and learned to take it to the limit /

Hello, curious steemers

I announced the foundations of math series in the video in
Steemit series on Mathematics, Types & Quantum electrodynamics
and posted the first proper episode. Today I do a fun post instead. Two days and we're already toying around ;)

If you haven't ever heard of "this issue" discussed here before, peek at this Wikipedia article first. Or jump right in and check it out afterwards. One great video that ties to this post is by the youtuber 3Blue1Brown. He is (as far as I can tell) the best youtube channel on popular math and gets as "-1/12" from a complex analysis angle (pun intended).

The video also makes me not have to choose a screencap for this post, haha.

So I wrote this in my notebook and included images, as it seems steemitdoesn't provide simple math formatting yet. Please point it out when I'm just misinformed, there, as I hope.

My post is basically about the following graph. The line goes to negative -1/12 and I'll try to make clear what's happening.

If you know limits well, the answer is in this computer output:

But don't mind for the moment. Let's get down to business...

In closing, I want to provide some Wikipedia links to some topics mentioned above:

• Euler–Maclaurin formula
• Logarithm
• 1+2+3+4+... article

And then there is a wide range of theories of infinite summation which differ from the standard one in analysis. I can do more about this, but maybe check out Borel summation as a starting point. The Ramanujan summation is the one most closely tied to the Euler–Maclaurin formula. Another video by 3blue1brown that can be seen to tie to this post is the following:

This guy does fantastic animations, and indeed he even published the Python code he uses and encourages you to play around with it. His code is located at this github repo. For example, he's a gif for my own channel *wink*
If someone is interest, I may make a steemit post on how to use that package.

Please help me figure out in which direction I should go with those posts.

Take care! :)