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A362662 Decimal expansion of Sum_{n>=1} (tan(1/n) - sin(1/n)). 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A073442 A177428 A130617 * A010150 A176153 A136711
KEYWORD
nonn,cons
AUTHOR
Bernard Schott, Apr 29 2023
STATUS
approved

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Last modified April 19 19:02 EDT 2024. Contains 371798 sequences. (Running on oeis4.)