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A277754
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Decimal expansion of Sum_{n>=1} sin((n*Pi)/3)^n.
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2
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2, 9, 2, 5, 6, 4, 0, 8, 4, 6, 1, 0, 7, 1, 4, 2, 7, 5, 9, 7, 1, 3, 0, 8, 7, 8, 0, 4, 8, 9, 4, 1, 1, 3, 8, 6, 8, 5, 7, 2, 9, 5, 3, 3, 3, 9, 2, 7, 9, 6, 0, 3, 4, 8, 0, 8, 8, 5, 9, 8, 1, 0, 1, 9, 2, 5, 2, 0, 8, 2, 7, 6, 3, 1, 5, 4, 6, 8, 1, 0, 9, 5, 1, 1, 1, 7
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OFFSET
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1,1
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COMMENTS
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The sum of four easily recognized geometric series that have common ratio 9/64.
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LINKS
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FORMULA
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Equals (14/37)*(6 + sqrt(3)).
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EXAMPLE
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2.92564084610714275971308780...
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MATHEMATICA
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r = Sqrt[3]/2; u = Simplify[r (1 + r + r^3 - r^4)/(1 - r^6)]
RealDigits[N[u, 120], 10][[1]]
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PROG
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(PARI) suminf(n=1, sin((n*Pi)/3)^n) \\ Michel Marcus, Oct 29 2016
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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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