Infinite Series - Numberphile

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Fields Medallist Charlie Fefferman talks about some classic infinite series.
More links & stuff in full description below ↓↓↓

NUMBERPHILE

Videos by Brady Haran
Editing and animation by Pete McPartlan

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Hello, you can't end it like that. Not without explaining how it becomes Pi^2/6

snowgw

Introducing the Numberphile video channel which absolutely will never, ever be discontinued - The Infinite Series.

JJ-kleq

can I just compliment the animations in this video? in terms of presentation, numberphiles has come such a long way, and I love it!

Kilroyan

Shout out to whoever did the work of adding the animation of an enormous sum that only stays on screen for about 2 seconds. You're the hero. Or depending on how it was edited, the person who wrote it out. Edit: And the person doing the 3D animations.

zuzusuperfly

Matt Parker used this series and equation to calculate pi on pi-day with multiple copies of his book named Humble Pi.

erumaayuuki

My mind cannot handle the different kind of paper!

ilyrm

"PI creeps in where you would least expect it..." and so does this video.

CCarrMcMahon

Another fun bit of mathematics related to this topic:
In the video, it is explained that 1 + (1/2) + (1/3) + ... diverges and that 1 + (1/2)^2 + (1/3)^2 + ... converges.
So for a value s, somewhere between 1 and 2, you could expect there to be a turning point such that 1 + (1/2)^s + (1/3)^s + ... switches from being divergent to being convergent.

This turning point happens to be s = 1. That means that for any value of s greater than 1, the series converges.
Therefore, even something like 1 + (1/2)^1.001 + (1/3)^1.001 + ... converges.

maxpeeters

An infinite number of mathematicians enter a bar. The first one orders one beer, the second one orders half a beer, the third orders a quarter of a beer, the fourth orders an eighth of a beer, and so on. After taking orders for a while, the bartender sighs exasperatedly, says, "You guys need to know your limits, " and pours two beers for the whole group.

ruhrohraggy