A362662 - OEIS

%I #19 May 05 2023 05:00:39

%S 8,2,2,0,8,2,2,0,0,8,0,3,5,8,8,2,0,2,9,3,5,8,7,0,1,1,8,7,1,5,9,9,3,5,

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

%U 1,0,5,3,4,5,3,5,4,3,6,8,1,3,2,4,6,0,0,4,7,1,3,4,7,4,3,2,2

%N Decimal expansion of Sum_{n>=1} (tan(1/n) - sin(1/n)).

%C Series Sum_{n>=1} sin(1/n) and Sum_{n>=1} tan(1/n) -> oo but with u(n) = (tan(1/n) - sin(1/n)), as u(n) ~ 1 / (2*n^3) when n -> oo, the series Sum_{n>=1} u(n) is convergent.

%D J. Guégand and M.-A. Maingueneau, Exercices d'Analyse, Exercice 1 - 41.2, p. 47, Classes Préparatoires aux Grandes Ecoles, Ellipses, 1988.

%e Equals 0.822082200803588202935870118715993520730...

%p evalf(sum(tan(1/n) - sin(1/n), n=1..infinity), 120);

%o (PARI) sumpos(n=1, tan(1/n) - sin(1/n)) \\ _Michel Marcus_, Apr 29 2023

%Y Cf. A096444, A248946, A248948, A342680.

%K nonn,cons

%O 0,1

%A _Bernard Schott_, Apr 29 2023