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A362752 Decimal expansion of Sum_{k>=1} (1/k - sin(1/k)).

%I A362752 #7 May 02 2023 11:11:17
%S A362752 1,9,1,8,9,9,0,8,5,5,0,6,2,6,4,8,2,7,9,8,1,1,4,6,0,7,7,2,2,6,4,3,9,8,
%T A362752 4,3,4,0,4,3,0,9,1,0,2,3,7,7,5,5,0,9,5,3,9,1,1,7,2,1,2,9,8,0,9,0,7,7,
%U A362752 4,8,0,1,2,3,5,1,3,4,0,8,1,2,1,7,0,4,9,4,4,0,2,5,4,2,8,1,6,2,6,8,1,1,7,8,5
%N A362752 Decimal expansion of Sum_{k>=1} (1/k - sin(1/k)).
%H A362752 Math Stackexchange, <a href="https://math.stackexchange.com/questions/51757/closed-form-for-sum-k-1n-sin-frac1k">Closed Form for Sum_{k=1..n} sin(1/k)</a>, 2011.
%F A362752 Equals Sum_{k>=1} (-1)^(k+1)*zeta(2*k+1)/(2*k+1)!.
%e A362752 0.19189908550626482798114607722643984340430910237755...
%p A362752 evalf(sum(1/k - sin(1/k), k = 1..infinity), 120);
%o A362752 (PARI) sumalt(k = 1, (-1)^(k+1) * zeta(2*k+1)/(2*k+1)!)
%Y A362752 Cf. A233383, A248945, A248946, A249022, A362753.
%K A362752 nonn,cons
%O A362752 0,2
%A A362752 _Amiram Eldar_, May 02 2023