A354222 Decimal expansion of 2 / (Pi+2).

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

Offset: 0

Author

Bernard Schott, May 19 2022

Keywords

• nonn
• cons

Comments

The sequence u(n+1) = 1 / ( u(n) + 1/(n+1) ) with u(0) >= 0 is convergent with lim_{n->oo} u(n) = 1; however, this sequence is monotonic iff u(0) = 2 / (Pi+2), and in this case, this sequence is increasing.

Examples

			0.388984529648342710619404612046031138262577367...
		

References

• J. M. Arnaudiès, P. Delezoide et H. Fraysse, Exercices résolus d'Analyse du cours de mathématiques - 2, Dunod, 1993, Exercice 1, pp. 29-35.

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A060294, A197686.

Programs

Maple

evalf(2/(Pi+2), 100);

Mathematica

RealDigits[2/(Pi + 2), 10, 100][[1]] (* Amiram Eldar, May 19 2022 *)

PARI

2/(Pi+2) \\ Michel Marcus, May 20 2022

Formula

Equals 1 - A197686.