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A239545 Decimal expansion of Sum_{k>=0} (-1)^k/((2k+1)*(2k+3)*(2k+5)). 0

%I #12 Jul 04 2020 05:51:44

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

%T 2,7,1,9,1,3,1,2,8,4,1,5,8,8,5,5,4,8,9,4,2,8,8,5,3,4,7,4,0,7,0,5,1,4,

%U 3,7,1,7,4,5,2,4,4,2,7,9,1,4,9,5,1,7,1,0

%N Decimal expansion of Sum_{k>=0} (-1)^k/((2k+1)*(2k+3)*(2k+5)).

%D L. B. W. Jolley, Summation of series, Dover Publications Inc. (New York), 1961, p. 44 (series n. 240).

%F Equals Pi/8 - 1/3 = A019675 - A010701.

%F Equals Sum_{k>=1} 1/((4*k+1)*(4*k+3)) = Sum_{k>=1} 1/A001539(k). - _Amiram Eldar_, Jul 04 2020

%e 0.0593657483653908214744970895766045271913128415885548942885347407051...

%t RealDigits[Pi/8 - 1/3, 10, 90, -1][[1]]

%o (PARI) Pi/8-1/3 \\ _Charles R Greathouse IV_, May 05 2014

%Y Cf. A000796, A001539, A005408 (odd numbers) A021016 (Sum_{k>=0} 1/((2k+1)*(2k+3)*(2k+5))), A061550.

%K nonn,cons

%O 0,2

%A _Bruno Berselli_, Mar 21 2014

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