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A242024
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Decimal expansion of Sum_{n>=1} (-1)^(n+1)*6/(n*(n+1)*(n+2)).
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6
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8, 1, 7, 7, 6, 6, 1, 6, 6, 7, 1, 9, 3, 4, 3, 7, 1, 3, 0, 0, 6, 7, 8, 5, 4, 5, 7, 4, 9, 8, 1, 1, 8, 8, 1, 6, 9, 0, 6, 0, 0, 1, 6, 1, 2, 3, 2, 3, 0, 6, 3, 0, 4, 9, 4, 4, 8, 1, 6, 0, 1, 1, 3, 9, 2, 0, 7, 2, 3, 4, 6, 3, 6, 3, 6, 3, 3, 6, 5, 8, 7, 2, 7, 0, 3, 5, 9, 9, 2, 3, 9, 5, 7
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OFFSET
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0,1
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COMMENTS
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The sum of the reciprocals of binomial(n,3) for n >= 3 (or A000292(n), for n >= 1) with alternating signs.
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LINKS
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FORMULA
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Equals 12*log(2) - 15/2.
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EXAMPLE
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0.8177661667193437130067854...
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MATHEMATICA
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RealDigits[Chop[Sum[N[(-1)^(n+1)*6/(n*(n+1)*(n+2)), 150], {n, 1, Infinity}]], 10, 120][[1]] (* Harvey P. Dale, Jun 02 2016 *)
RealDigits[12*Log[2] - 15/2, 10, 120][[1]] (* Amiram Eldar, Jun 20 2023 *)
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PROG
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(PARI) sumalt(n=1, (-1)^(n + 1)*6/(n*(n + 1)*(n + 2))) \\ Michel Marcus, Aug 14 2014
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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