OFFSET
0,1
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.
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.
FORMULA
Equals 1 - A197686.
EXAMPLE
0.388984529648342710619404612046031138262577367...
MAPLE
evalf(2/(Pi+2), 100);
MATHEMATICA
RealDigits[2/(Pi + 2), 10, 100][[1]] (* Amiram Eldar, May 19 2022 *)
PROG
(PARI) 2/(Pi+2) \\ Michel Marcus, May 20 2022
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Bernard Schott, May 19 2022
STATUS
approved