ASTOUNDING: 1 + 2 + 3 + 4 + 5 + ... = -1/12

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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: http://youtu.be/E-d9mgo8FGk MORE: http://youtu.be/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.... http://www.youtube.com/watch?v=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. Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9 Numberphile T-Shirts: https://teespring.com/stores/numberphile Other merchandise: https://store.dftba.com/collections/numberphile