OFFSET
0,2
LINKS
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
KEYWORD
nonn,cons
AUTHOR
Claude H. R. Dequatre, Nov 20 2022
STATUS
approved