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
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Kyle
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