A239362 Decimal expansion of Sum_{k>=1} 1/((3k-2)*(3k-1)*(3k)).

1, 7, 8, 7, 9, 6, 7, 6, 8, 8, 9, 1, 5, 2, 7, 0, 3, 9, 7, 9, 9, 7, 0, 8, 2, 5, 5, 1, 7, 9, 9, 0, 7, 5, 0, 6, 9, 0, 9, 1, 4, 3, 9, 2, 2, 5, 6, 7, 4, 9, 7, 7, 8, 0, 9, 5, 8, 7, 9, 7, 6, 5, 0, 4, 3, 7, 6, 5, 7, 2, 2, 1, 9, 7, 6, 9, 3, 6, 2, 2, 9, 2, 0, 2, 6, 2, 7

Offset

0,2

References

L. B. W. Jolley, Summation of series, Dover Publications Inc. (New York), 1961, p. 46 (series n. 250).

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Formula

Equals ( Pi*sqrt(3)/3 - log(3) )/4.

Example

0.1787967688915270397997082551799075069091439225674977809587976504...
1/(1*2*3) + 1/(4*5*6) + 1/(7*8*9) + 1/(10*11*12) + 1/(13*14*15) + ...

Maple

evalf[100]((Pi*sqrt(3) - 3*log(3))/12 ); # G. C. Greubel, Aug 11 2019

Mathematica

RealDigits[(Pi Sqrt[3]/3 - Log[3])/4, 10, 100][[1]]

Prog

(PARI) default(realprecision, 100); (Pi*sqrt(3) - 3*log(3))/12 \\ G. C. Greubel, Aug 11 2019
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (Pi(R)*Sqrt(3) - 3*Log(3))/12; // G. C. Greubel, Aug 11 2019
(Sage) numerical_approx((pi*sqrt(3) - 3*log(3))/12, digits=100) # G. C. Greubel, Aug 11 2019

Crossrefs

Cf. A164833: Sum_{k>=1} 1/((4k-2)*(4k-1)*(4k)).

Sequence in context: A010728 A291509 A153856 * A094819 A019861 A065470

Adjacent sequences: A239359 A239360 A239361 * A239363 A239364 A239365

Keyword

nonn,cons

Author

Bruno Berselli, Mar 17 2014

Status

approved