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

%I A239362 #15 Jun 21 2024 14:41:24
%S A239362 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,
%T A239362 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,
%U A239362 7,2,2,1,9,7,6,9,3,6,2,2,9,2,0,2,6,2,7
%N A239362 Decimal expansion of Sum_{k>=1} 1/((3k-2)*(3k-1)*(3k)).
%D A239362 L. B. W. Jolley, Summation of series, Dover Publications Inc. (New York), 1961, p. 46 (series n. 250).
%H A239362 G. C. Greubel, <a href="/A239362/b239362.txt">Table of n, a(n) for n = 0..10000</a>
%H A239362 Anthony Sofo, <a href="https://doi.org/10.1007/s13226-019-0313-z">Euler related binomial sums</a>, Indian J. Pure Appl. Math. 50 (1) (2019) 149-160, S(3).
%F A239362 Equals ( Pi*sqrt(3)/3 - log(3) )/4.
%e A239362 0.1787967688915270397997082551799075069091439225674977809587976504...
%e A239362 1/(1*2*3) + 1/(4*5*6) + 1/(7*8*9) + 1/(10*11*12) + 1/(13*14*15) + ...
%p A239362 evalf[100]((Pi*sqrt(3) - 3*log(3))/12 ); # _G. C. Greubel_, Aug 11 2019
%t A239362 RealDigits[(Pi Sqrt[3]/3 - Log[3])/4, 10, 100][[1]]
%o A239362 (PARI) default(realprecision, 100); (Pi*sqrt(3) - 3*log(3))/12 \\ _G. C. Greubel_, Aug 11 2019
%o A239362 (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (Pi(R)*Sqrt(3) - 3*Log(3))/12; // _G. C. Greubel_, Aug 11 2019
%o A239362 (Sage) numerical_approx((pi*sqrt(3) - 3*log(3))/12, digits=100) # _G. C. Greubel_, Aug 11 2019
%Y A239362 Cf. A164833: Sum_{k>=1} 1/((4k-2)*(4k-1)*(4k)).
%K A239362 nonn,cons
%O A239362 0,2
%A A239362 _Bruno Berselli_, Mar 17 2014