This one was too hard for me, so I dug around a bit and found that it's a special case of a more general formula from Ramanujan (and in fact this specific problem was given by Ramanujan). You can read about it here (skip down to where it says "Ramanujan posed this problem to the 'Journal of Indian Mathematical Society'"): http://en.wikipedia.org/wiki/Nested_radical#Some_identities_of_Ramanujan And also here (look for "Ramanjuan discovered" followed by equation (26) - I used 25 in the URL below to position the page just above it without cutting off the top): http://mathworld.wolfram.com/NestedRadical.html#eqn25 Tom On 8/14/10, Fred lunnon <fred.lunnon@gmail.com> wrote:
This one is very nice --- but unless I've missed something (again!), it does seem an awful lot harder than the others on this page! WFL
On 8/14/10, Joshua Zucker <joshua.zucker@gmail.com> wrote:
On somewhat the same topic, how about problem 6 at http://www.msri.org/specials/festival/activities/InfinityFinite.pdf ?
--Joshua Zucker
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