%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