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%I #18 May 26 2022 13:16:35
%S 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,
%T 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,
%U 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
%N Decimal expansion of 2 / (Pi+2).
%C 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.
%D J. M. Arnaudiès, P. Delezoide et H. Fraysse, Exercices résolus d'Analyse du cours de mathématiques - 2, Dunod, 1993, Exercice 1, pp. 29-35.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals 1 - A197686.
%e 0.388984529648342710619404612046031138262577367...
%p evalf(2/(Pi+2), 100);
%t RealDigits[2/(Pi + 2), 10, 100][[1]] (* _Amiram Eldar_, May 19 2022 *)
%o (PARI) 2/(Pi+2) \\ _Michel Marcus_, May 20 2022
%Y Cf. A060294, A197686.
%K nonn,cons
%O 0,1
%A _Bernard Schott_, May 19 2022
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