

A354238


Decimal expansion of 1  Pi^2/12.


1



1, 7, 7, 5, 3, 2, 9, 6, 6, 5, 7, 5, 8, 8, 6, 7, 8, 1, 7, 6, 3, 7, 9, 2, 4, 1, 6, 6, 7, 6, 9, 8, 7, 4, 0, 5, 3, 9, 0, 5, 2, 5, 0, 4, 9, 3, 9, 6, 6, 0, 0, 7, 8, 1, 1, 3, 2, 2, 2, 0, 8, 8, 5, 3, 1, 4, 9, 9, 6, 2, 6, 4, 7, 9, 8, 3, 9, 9, 5, 6, 3, 0, 8, 3, 1, 8, 5, 5, 4, 9, 6, 9, 0, 1, 2, 0, 6, 4, 7, 3, 4, 7, 9, 9, 7
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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. 296298.


FORMULA

Equals lim_{n>infinity} A004125(n)/(n^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


EXAMPLE

0.177532966575886781763792416676987405390525049396600781132220885314996264798...


MATHEMATICA

RealDigits[1  Pi^2/12, 10, 100][[1]] (* Amiram Eldar, May 20 2022 *)


PROG

(PARI) 1Pi^2/12
(PARI) 1zeta(2)/2


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



