A226735 - OEIS

A226735

Decimal expansion of Sum_{k>=0} (-1)^k * (3*k + 1)^(-3).

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

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..104.

R. W. Gosper, Acceleration of series, AI memo 304 (1974), page 40

FORMULA

Equals (10*Sqrt(3)*Pi^3 + 351*zeta(3))/972.

EXAMPLE

0.986590986262542291303205534145739320952044749668716985997437418...

MATHEMATICA

RealDigits[N[Sum[(-1)^k (3k + 1)^(-3), {k, 0, Infinity}], 10, 105]][[1]] (* Grau, corrected by Alonso del Arte, Jan 01 2014 *)