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

0,2

Links

Table of n, a(n) for n=0..104.

Math Stackexchange, Closed Form for Sum_{k=1..n} sin(1/k), 2011.

Formula

Equals Sum_{k>=1} (-1)^(k+1)*zeta(2*k+1)/(2*k+1)!.

Example

0.19189908550626482798114607722643984340430910237755...

Maple

evalf(sum(1/k - sin(1/k), k = 1..infinity), 120);

Prog

(PARI) sumalt(k = 1, (-1)^(k+1) * zeta(2*k+1)/(2*k+1)!)

Crossrefs

Cf. A233383, A248945, A248946, A249022, A362753.

Sequence in context: A198758 A075700 A021843 * A231931 A175615 A200696

Adjacent sequences: A362749 A362750 A362751 * A362753 A362754 A362755

Keyword

nonn,cons

Author

Amiram Eldar, May 02 2023

Status

approved