A242024 Decimal expansion of Sum_{n>=1} (-1)^(n+1)*6/(n*(n+1)*(n+2)).

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

Offset: 0

Author

Richard R. Forberg, Aug 11 2014

Keywords

• nonn
• cons

Comments

The sum of the reciprocals of binomial(n,3) for n >= 3 (or A000292(n), for n >= 1) with alternating signs.

Also see A242023.

Examples

			0.8177661667193437130067854...
		

Crossrefs

Cf. A242023, A000217, A000292, A000332, A002162.

Programs

Mathematica

RealDigits[Chop[Sum[N[(-1)^(n+1)*6/(n*(n+1)*(n+2)),150],{n,1,Infinity}]], 10,120][[1]] (* Harvey P. Dale, Jun 02 2016 *)
RealDigits[12*Log[2] - 15/2, 10, 120][[1]] (* Amiram Eldar, Jun 20 2023 *)

PARI

12*log(2) - 15/2 \\ Michel Marcus, Aug 13 2014

PARI

sumalt(n=1, (-1)^(n + 1)*6/(n*(n + 1)*(n + 2))) \\ Michel Marcus, Aug 14 2014

Formula

Equals 12*log(2) - 15/2.

Extensions

Prior Mathematica program replaced by Harvey P. Dale, Jun 02 2016