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Decimal expansion of Sum_{k>=0} (sin(k*Pi/5))^2/2^k.
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%I #8 Jul 16 2024 12:01:24

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

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

%U 1,9,1,3,0,8,9,4,0,7,9,4,5,9,8,1,9,0

%N Decimal expansion of Sum_{k>=0} (sin(k*Pi/5))^2/2^k.

%C Minimal polynomial is 124x^2 - 150x + 45. - _Charles R Greathouse IV_, Jul 16 2024

%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>

%F Equals (3/124) (25 - sqrt(5)).

%e 0.5507402908669405718610683789823078330135334267835...

%t s = Sum[(Sin[k Pi/5])^2/2^k, {k, 0, Infinity}]

%t d = N[s, 100]

%t First[RealDigits[d]]

%o (PARI) suminf(k=0,(sin(k*Pi/5))^2>>k) \\ _Charles R Greathouse IV_, Jul 16 2024

%o (PARI) (75-sqrt(45))/124 \\ _Charles R Greathouse IV_, Jul 16 2024

%Y Cf. A373021.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Jul 16 2024