Mensaje citado por: asimovd@aol.com:
I think this is an old problem, almost certainly solved, but I don't think I've ever seen the solution:
Given the harmonic series but with an independently chosen random sign in front of each term:
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a. what is the probability of convergence? b. when it converges, what is the probability distribution of the sum?
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You're right about this being an old problem, as well as the implicit "but nobody remembers the solution or where they saw it." This is all the more embarassing because I am just now teaching a complex variable course, and have just told them about gap and density theorems, including the part where randomizing signs in the geometric series almost surely creates a lacunary function which in no way will extend beyond the unit circle. References at hand aren't much help answering your specific questions; maybe a search via Google or Math Reviews or something would turn up something, but the casual look I have had hasn't turned up anything. - hvm ------------------------------------------------- Obtén tu correo en www.correo.unam.mx UNAMonos Comunicándonos