video thumbnail 7:50
ASTOUNDING: 1 + 2 + 3 + 4 + 5 + ... = -1/12

2014-01-09

[public] 8.21M views, 121K likes, 17.5K dislikes audio only

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Read this too: http://www.bradyharanblog.com/blog/2015/1/11/this-blog-probably-wont-help

More links & stuff in full description below ↓↓↓

EXTRA ARTICLE BY TONY: http://bit.ly/TonyResponse

The sum of all natural numbers (from 1 to infinity) produces an "astounding" result.

ANOTHER PROOF & EXTRA FOOTAGE: /youtube/video/E-d9mgo8FGk

MORE: /youtube/video/0Oazb7IWzbA

NY Times article on this: http://nyti.ms/1iftqSv

Tony Padilla and Ed Copeland are physicists at the University of Nottingham.

They talk physics at our sixty symbols channel: http://www.youtube.com/sixtysymbols

Grandi's Series: 1-1+1-1.... /youtube/video/PCu_BNNI5x4

Read more about divergent series: http://en.wikipedia.org/wiki/Divergent_series

We also hear that Chapter XIII of Konrad Knopp's book, "Theory and Application of Infinite Sequences and Series", is very good if you can get your hands on it.

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Intro
/youtube/video/w-I6XTVZXww?t=0
Statement
/youtube/video/w-I6XTVZXww?t=44
Steps
/youtube/video/w-I6XTVZXww?t=72
Attach a number
/youtube/video/w-I6XTVZXww?t=112
Find the sum
/youtube/video/w-I6XTVZXww?t=167
Subtract
/youtube/video/w-I6XTVZXww?t=255
Formula
/youtube/video/w-I6XTVZXww?t=327
Sum of Natural Numbers (second proof and extra footage) 1,666,643 views
/youtube/video/E-d9mgo8FGk
Why -1/12 is a gold nugget 2,638,985 views
/youtube/video/0Oazb7IWzbA
One minus one plus one minus one - Numberphile 4,561,603 views
/youtube/video/PCu_BNNI5x4