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

Numberphile
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9.3M views 11 years ago
Read this too: http://www.bradyharanblog.com/blog/20... 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:    • Sum of Natural Numbers (second proof ...   MORE:    • Why -1/12 is a gold nugget   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:    / sixtysymbols   Grandi's Series: 1-1+1-1....    • One minus one plus one minus one - Nu...   Read more about divergent series: http://en.wikipedia.org/wiki/Divergen... 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:   / numberphile   NUMBERPHILE Website: http://www.numberphile.co …...more
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ASTOUNDING: 1 + 2 + 3 + 4 + 5 + ... = -1/12
124KLikes
9,332,530Views
2014Jan 9
Read this too: http://www.bradyharanblog.com/blog/20... 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:    • Sum of Natural Numbers (second proof ...   MORE:    • Why -1/12 is a gold nugget   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:    / sixtysymbols   Grandi's Series: 1-1+1-1....    • One minus one plus one minus one - Nu...   Read more about divergent series: http://en.wikipedia.org/wiki/Divergen... 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:   / numberphile   NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook:   / numberphile   Numberphile tweets:   / 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:   / 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/n...

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Numberphile

4.64M subscribers