Strange/Interesting Mathematical Phenomena

[Kid Gambino]

I thought this one was really cool. VSauce is always worth a watch.

 

https://www.youtube.com/watch?v=J51ncHP_BrY

That video was not quick mafs, but I enjoyed it nonetheless. Kinda made me miss being a math wiz.

[Nathanael D. Striker]

1 + 2 + 3 + 4 + 5 + 6 + ......... = -1/12

 

Strangely enough, I had an Engineering PhD student show me the proof of that last weekend. Very interesting indeed, and it does give different contexts for infinity.

[EHN.]

Thoughts on my integration idea

 

Must have been a crazy s*** to make you want to start integrating by parts repeatedly. Though I'm guessing you were doing a different problem involving it and realised that there's some cool patterns with integration by parts a bunch of times. It's pretty funking cool that you'd think to come up with this from it though.

 

I wrote it down and had a look, only problem I can see is that there should be a remainder term which we have to assume is always 0 but that isn't always the case here so I don't think the radius of convergence is infinite. Gonna revisit this later when my brain is feeling a bit less fried. 

[Ryusei the Morning Star]

Must have been a crazy s*** to make you want to start integrating by parts repeatedly. Though I'm guessing you were doing a different problem involving it and realised that there's some cool patterns with integration by parts a bunch of times. It's pretty funking cool that you'd think to come up with this from it though.

 

I wrote it down and had a look, only problem I can see is that there should be a remainder term which we have to assume is always 0 but that isn't always the case here so I don't think the radius of convergence is infinite. Gonna revisit this later when my brain is feeling a bit less fried. 

Well it was coming out in parts, that much is certain

[Nathanael D. Striker]

Must have been a crazy s*** to make you want to start integrating by parts repeatedly. Though I'm guessing you were doing a different problem involving it and realised that there's some cool patterns with integration by parts a bunch of times. It's pretty funking cool that you'd think to come up with this from it though.

 

I wrote it down and had a look, only problem I can see is that there should be a remainder term which we have to assume is always 0 but that isn't always the case here so I don't think the radius of convergence is infinite. Gonna revisit this later when my brain is feeling a bit less fried.

Thanks for this. I thought about verifying it myself, but I got more midterms to worry about. X___X