A358519 Decimal expansion of Sum_{k >= 1} (-1)^(k+1)/(k^2 + 4*k - 1).

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

Offset

0,2

Links

Table of n, a(n) for n=0..94.

Michael I. Shamos, A catalog of the real numbers (2011), p. 253.

Formula

Equals Sum_{k >=1} (-1)^(k+1)/(k^2 + 4*k - 1).

Equals (Pi/(2*sqrt(5)))*csc(Pi*sqrt(5)) - 17/20 = Sum_{k>=3} (-1)^(k+1)/(k^2-5). [from the Shamos reference]

Equals Sum_{k>=3} (-1)^(k+1)/A028875(k). - Amiram Eldar, Nov 21 2022

Example

0.189957907718062725271908409063636655279566491...

Mathematica

RealDigits[(2*Sqrt[5]*Pi*Csc[Sqrt[5]*Pi] - 17)/20, 10, 120][[1]] (* Amiram Eldar, Nov 21 2022 *)

Prog

(PARI) (Pi/(2*sqrt(5)))*1/sin(Pi*sqrt(5)) - 17/20

Crossrefs

Cf. A028875, A242023, A242024, A358516, A358517.

Cf. A002162.

Sequence in context: A244959 A345987 A241990 * A256923 A347219 A320304

Adjacent sequences: A358516 A358517 A358518 * A358520 A358521 A358522

Keyword

nonn,cons

Author

Claude H. R. Dequatre, Nov 20 2022

Status

approved