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Decimal expansion of Sum_{n>=1} |sin((n*Pi)/3)|^n.
2

%I #12 Dec 12 2023 18:34:06

%S 4,6,1,0,8,7,9,4,6,9,6,8,7,6,7,2,0,1,8,2,8,0,3,3,2,8,9,3,9,2,6,8,5,4,

%T 5,4,9,9,2,2,7,0,9,8,0,2,4,4,6,4,6,0,3,0,8,1,8,3,5,2,2,9,4,5,2,0,5,3,

%U 1,4,8,8,7,7,1,4,5,9,4,6,4,4,7,0,4,2

%N Decimal expansion of Sum_{n>=1} |sin((n*Pi)/3)|^n.

%H Michelle Huff, <a href="/A277755/b277755.txt">Table of n, a(n) for n = 1..10000</a>

%e (2/37)*(42 + 25 Sqrt[3]) = 4.61087946968767201828033289392685454992..., the sum of two easily recognized geometric series that have common ratio (3/4)^(3/2).

%t r = Sqrt[3]/2; u = Simplify[r (1 + r)/(1 - r^3)]

%t RealDigits[N[u, 1200], 10][[1]]

%o (PARI) suminf(n=1, abs(sin((n*Pi)/3))^n) \\ _Michel Marcus_, Oct 29 2016

%Y Cf. A010527, A277754.

%K nonn,cons

%O 1,1

%A _Michelle Huff_, Oct 28 2016