Ok, this one I can do: n = sqrt(1/2^(2^0) + sqrt(1/2^(2^1) + sqrt(1/2^(2^2) + ...))) (1/sqrt(2))*n = sqrt(1/2^(2^1) + sqrt(1/2^(2^2) + sqrt(1/2^(2^3) + ...))) n = sqrt(1/2^(2^0) + (1/sqrt(2))*n) n^2 = 1/2 + (1/sqrt(2))*n sqrt(2)*n^2 - n - sqrt(2)/2 = 0 Discarding the negative solution: n = (1 + sqrt(5)) / (2*sqrt(2)) This is also the golden ratio divided by sqrt(2): n = phi / sqrt(2) Tom
Find a closed form for the the expression
sqrt(1/2^(2^0) + sqrt(1/2^(2^1) + sqrt(1/2^(2^2) + ...))).
--Dan
P.S. No fair using electronic assistance.
_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele
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