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A337911
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Decimal expansion of probability that the random harmonic series converges to 0.
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0
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OFFSET
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0,1
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COMMENTS
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Define g(0, x) = 1/4 if -2 <= x <= 2, otherwise g(0, x) = 0; g(n, x) = Integral_{y=x - 2/(2*n+1)..x + 2/(2*n+1)} g(n - 1, y)*(2*n+1)/4 dy for n > 0. With t_i being independent random variables with common distribution P(t_i = 1) = P(t_i = -1) = 1/2, the probability of random harmonic series Sum_{i>=1} (t_i)/i converging to x is lim_{n->infinity} g(n, x).
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LINKS
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Byron Schmuland, Random Harmonic Series, The American Mathematical Monthly, Vol. 110, No. 5 (May, 2003), pp. 407-416.
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EXAMPLE
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0.249915039...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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