A196548 Decimal expansion of Sum_{i>=0} 1/((6*i+2)*(6*i+5)).

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

Offset: 0

Author

R. J. Mathar, Oct 03 2011

Keywords

• nonn
• cons
• easy

Comments

Sum of the inverse elements of the sequence 10, 88, 238, 460, 754, 1120, 1558,...

Examples

			0.124516909297141393464094015131553...
		

References

• L. B. W. Jolley, Summation of Series, Dover, 1961, eq. (263) on page 48.
• J. Rivaud, Analyse, Séries, équations différentielles, Mathématiques supérieures et spéciales, Premier cycle universitaire, Vuibert, 1981, Exercice 3, p. 132.

Crossrefs

Cf. A093602, A002162, A193534.

Programs

Maple

(Pi/sqrt(3)-log(2))/9 ; evalf(%) ;

Mathematica

RealDigits[(Pi/Sqrt[3] - Log[2])/9, 10, 75][[1]] (* Bruno Berselli, Dec 20 2011 *)

Formula

Equals (Pi/sqrt(3)-log(2))/9 = 1/(2*5) +1/(8*11) +1/(14*17)+...

Equals (1/3) * A193534. - Bernard Schott, Jan 28 2022