OFFSET
0,1
COMMENTS
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.
REFERENCES
J. Guégand and M.-A. Maingueneau, Exercices d'Analyse, Exercice 1 - 41.2, p. 47, Classes Préparatoires aux Grandes Ecoles, Ellipses, 1988.
EXAMPLE
Equals 0.822082200803588202935870118715993520730...
MAPLE
evalf(sum(tan(1/n) - sin(1/n), n=1..infinity), 120);
PROG
(PARI) sumpos(n=1, tan(1/n) - sin(1/n)) \\ Michel Marcus, Apr 29 2023
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Bernard Schott, Apr 29 2023
STATUS
approved