A303658 Decimal expansion of the alternating sum of the reciprocals of the triangular numbers.

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

Offset: 0

Author

Jon E. Schoenfield, Apr 28 2018

Keywords

• nonn
• cons

Examples

			1/1 - 1/3 + 1/6 - 1/10 + 1/15 - 1/21 + ... = 0.77258872223978123766892848583270627230200053744102...
		

Crossrefs

Cf. A000217 (triangular numbers), A057711.

Apart from leading digit the same as A016639 (log(16)).

Programs

Mathematica

RealDigits[4*Log[2] - 2, 10, 100][[1]] (* Amiram Eldar, Aug 19 2020 *)
RealDigits[Log[16]-2,10,120][[1]] (* Harvey P. Dale, Apr 30 2022 *)

PARI

sumalt(n=1, (-1)^(n+1)*2/(n*(n+1))) \\ Michel Marcus, Apr 28 2018

PARI

log(16)-2 \\ Altug Alkan, May 07 2018

Formula

Equals log(16/e^2) = log(16) - 2.

Equals Sum_{k>=0} 1/((k+2)*2^k) = Sum_{k>=2} 1/A057711(k). - Amiram Eldar, Aug 19 2020

Equals 1 - Sum_{k>=1} 1/(k*(k+1)*(2*k+1)). - Davide Rotondo, May 24 2025