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