On 8/14/10, Tom Karzes <karzes@sonic.net> wrote:
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) + ...)))
Er ... don't follow this step, I'm afraid ... WFL
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.
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