OFFSET
0,2
COMMENTS
Ratio of area between the polygon that is adjacent in the same plane to the base of the stepped pyramid with an infinite number of levels described in A245092 and the circumscribed square (see the first formula).
LINKS
Ovidiu Furdui, Problem 1930, Mathematics Magazine, Vol. 86, No. 4 (2013), p. 289; A zeta series, Solution to Problem 1930 by Omran Kouba, ibid., Vol. 87, No. 4 (2014), pp. 296-298.
Paul J. Nahin, Inside interesting integrals, Undergrad. Lecture Notes in Physics, Springer (2020), (C7.4)
FORMULA
Equals lim_{n->infinity} A004125(n)/(n^2).
Equals 1 - A013661/2.
Equals 1 - A072691.
Equals A152416/2.
Equals Sum_{k>=1} 1/(2*k*(k+1)^2). - Amiram Eldar, May 20 2022
Equals -1/4 + Sum_{k>=2} (-1)^k * k * (k - Sum_{i=2..k} zeta(i)) (Furdui, 2013). - Amiram Eldar, Jun 09 2022
Equals integral_1^oo {x}/x^3 dx where {.} is the fractional part. [Nahin]. R. J. Mathar, May 22 2024
EXAMPLE
0.177532966575886781763792416676987405390525049396600781132220885314996264798...
MATHEMATICA
RealDigits[1 - Pi^2/12, 10, 100][[1]] (* Amiram Eldar, May 20 2022 *)
PROG
(PARI) 1-Pi^2/12
(PARI) 1-zeta(2)/2
CROSSREFS
KEYWORD
AUTHOR
Omar E. Pol, May 20 2022
STATUS
approved