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A363906 Decimal expansion of Sum_{n>=1} (arcsin(1/n) - sin(1/n)).

%I A363906 #22 Jun 29 2023 09:51:45
%S A363906 7,9,9,5,8,8,6,2,3,5,5,3,3,7,6,9,9,0,1,1,3,9,9,1,1,1,3,5,2,7,2,3,9,8,
%T A363906 2,5,0,4,0,1,7,2,2,8,4,1,9,0,7,7,7,9,6,8,3,6,4,1,1,6,5,9,2,8,4,3,6,7,
%U A363906 7,3,0,4,0,6,7,7,5,5,7,2,1,7,9,1,8,1,7
%N A363906 Decimal expansion of Sum_{n>=1} (arcsin(1/n) - sin(1/n)).
%C A363906 Series Sum_{n>=1} arcsin(1/n) and Sum_{n>=1} sin(1/n) -> oo but with v(n) = (arcsin(1/n) - sin(1/n)), as v(n) ~ 1 / (3*n^3) when n -> oo, the series Sum_{n>=1} v(n) is convergent.
%F A363906 Equals Sum_{k>=1} (binomial(2*k,k)/((2*k+1)*2^(2*k)) - (-1)^k/(2*k+1)!) * zeta(2*k+1). - _Vaclav Kotesovec_, Jun 27 2023
%e A363906 0.79958862355337699...
%t A363906 NSum[ArcSin[1/n]-Sin[1/n], {n, Infinity}, WorkingPrecision -> 95, NSumTerms -> 82] // RealDigits[#, 10, 87] &//First (* _Stefano Spezia_, Jun 27 2023 *)
%o A363906 (PARI) sumpos(n=1, asin(1/n) - sin(1/n)) \\ _Michel Marcus_, Jun 27 2023
%Y A363906 Cf. A096444, A248946, A342680, A362662.
%K A363906 nonn,cons
%O A363906 0,1
%A A363906 _Bernard Schott_, Jun 27 2023
%E A363906 More terms from _Stefano Spezia_, Jun 27 2023