A358516 Decimal expansion of Sum_{k >= 1} (-1)^(k+1)*1/((k+2)*(k+3)).

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

Offset

0,2

Links

Table of n, a(n) for n=0..93.

Michael I. Shamos, A catalog of the real numbers (2011) p.100.

Formula

Equals Sum_{k >= 1} (-1)^(k+1)*/((k+2)*(k+3)).

Equals 2*log(2) - 4/3 = Sum_{k >= 2} 1/(4*k^3 - k) = Sum_{k >= 1} (zeta(2*k + 1) - 1)/(4^k). [from the Shamos reference]

Equals Sum_{k >= 1} 1/((2^k)*(4*k + 12)). [from the Shamos reference]

Equals Sum_{k>=3} (-1)^(k+1)/A002378(k). - Amiram Eldar, Nov 21 2022

Example

0.0529610277865572855011309095830198028176669353...

Mathematica

Join[{0}, RealDigits[2*Log[2] - 4/3, 10, 120][[1]]] (* Amiram Eldar, Nov 21 2022 *)

Prog

(PARI) 2*log(2) - 4/3

Crossrefs

Cf. A002378, A242023, A242024, A358517, A358519.

Cf. A002162.

Sequence in context: A188933 A306648 A255655 * A177345 A209304 A367844

Adjacent sequences: A358513 A358514 A358515 * A358517 A358518 A358519

Keyword

nonn,cons

Author

Claude H. R. Dequatre, Nov 20 2022

Status

approved