A362752 Decimal expansion of Sum_{k>=1} (1/k - sin(1/k)).
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, 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, 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
Offset: 0
Examples
0.19189908550626482798114607722643984340430910237755...
Links
- Math Stackexchange, Closed Form for Sum_{k=1..n} sin(1/k), 2011.
Programs
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Maple
evalf(sum(1/k - sin(1/k), k = 1..infinity), 120);
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PARI
sumalt(k = 1, (-1)^(k+1) * zeta(2*k+1)/(2*k+1)!)
Formula
Equals Sum_{k>=1} (-1)^(k+1)*zeta(2*k+1)/(2*k+1)!.