# Can You Solve This Crazy Equation? Ramanujan's Radical Brain Teaser

## Description

In 1911, Srinivasa Ramanujan posed this problem involving an infinite nested radical (a never-ending expression that has square roots inside of square roots). Can you figure out how to simplify the equation? The video presents an intuitive solution. Technically it is necessary to prove the equation has a solution (the nested radical converges) because crazy things can happen with infinite expressions. The technical proof is included in a link below.

Blog post (text/image explanation). I also justify why the pattern continues for the first solution:

http://wp.me/p6aMk-4Dd

Technical proof

http://www.isibang.ac.in/~sury/ramanujanday.pdf

Intuitive proof algebra http://mathforum.org/library/drmath/view/52674.html

StackExchange discussion

http://math.stackexchange.com/questions/7204/limit-of-nested-radical-sqrt1-2-sqrt13-sqrt1-cdots

Thanks to Patrons!

Kyle

Alberto Nishikawa

Brian M. Mooney

If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions

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"Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.5/5 stars on 11 reviews. http://amzn.to/1GhUUSH

"Math Puzzles Volume 2" is a sequel book with more great problems. http://amzn.to/1NKbyCs

"Math Puzzles Volume 3" is the third in the series. http://amzn.to/1NKbGlp

"40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.9/5 stars on 7 reviews) http://amzn.to/1LOCI4U

"The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head http://amzn.to/18maAdo

"Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. http://amzn.to/XRm7M4

Blog post (text/image explanation). I also justify why the pattern continues for the first solution:

http://wp.me/p6aMk-4Dd

Technical proof

http://www.isibang.ac.in/~sury/ramanujanday.pdf

Intuitive proof algebra http://mathforum.org/library/drmath/view/52674.html

StackExchange discussion

http://math.stackexchange.com/questions/7204/limit-of-nested-radical-sqrt1-2-sqrt13-sqrt1-cdots

Thanks to Patrons!

Kyle

Alberto Nishikawa

Brian M. Mooney

If you like my videos, you can support me at Patreon: http://www.patreon.com/mindyourdecisions

Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you.

My Blog: http://mindyourdecisions.com/blog/

Twitter: http://twitter.com/preshtalwalkar

Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965

Google+: https://plus.google.com/108336608566588374147/posts

Pinterest: https://www.pinterest.com/preshtalwalkar/

Tumblr: http://preshtalwalkar.tumblr.com/

Instagram: https://instagram.com/preshtalwalkar/

Patreon: http://www.patreon.com/mindyourdecisions

Newsletter (sent about 2 times a year): http://eepurl.com/KvS0r

My Books

"The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 4/5 stars on 22 reviews) http://amzn.to/1uQvA20

"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. http://amzn.to/1o3FaAg

"Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.5/5 stars on 11 reviews. http://amzn.to/1GhUUSH

"Math Puzzles Volume 2" is a sequel book with more great problems. http://amzn.to/1NKbyCs

"Math Puzzles Volume 3" is the third in the series. http://amzn.to/1NKbGlp

"40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.9/5 stars on 7 reviews) http://amzn.to/1LOCI4U

"The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head http://amzn.to/18maAdo

"Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. http://amzn.to/XRm7M4

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