A362662 Decimal expansion of Sum_{n>=1} (tan(1/n) - sin(1/n)).

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, 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, 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

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.

Links

Table of n, a(n) for n=0..96.

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

Cf. A096444, A248946, A248948, A342680.

Sequence in context: A073442 A177428 A130617 * A010150 A176153 A136711

Adjacent sequences: A362659 A362660 A362661 * A362663 A362664 A362665

Keyword

nonn,cons

Author

Bernard Schott, Apr 29 2023

Status

approved