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, 6, 0, 5, 6, 0, 9, 7, 8, 7, 8, 3, 9, 3, 3, 2, 0, 6, 5, 9, 5, 0, 4
Offset: 0
Examples
0.0529610277865572855011309095830198028176669353...
Links
- Michael I. Shamos, A catalog of the real numbers (2011) p.100.
Programs
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Mathematica
Join[{0}, RealDigits[2*Log[2] - 4/3, 10, 120][[1]]] (* Amiram Eldar, Nov 21 2022 *) -
PARI
2*log(2) - 4/3
Formula
Equals Sum_{k >= 1} (-1)^(k+1)*/((k+2)*(k+3)) = A016627 -4/3.
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
Extensions
Missing terms 6, 0 inserted after a(74) by Georg Fischer, Feb 07 2025