A248948 -id:A248948 - cp's OEIS frontend

A248947 Decimal expansion of Sum_{n >= 1} tan(1/n)^2.

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

Offset: 1

Clark Kimberling, Oct 18 2014

			3.132799362818005226720034012858567638052280522418872401127192004180544...

Vaclav Kotesovec, Table of n, a(n) for n = 1..500

Cf. A248945, A248946, A248948.

evalf(sum((tan(1/n))^2, n=1..infinity), 120); # Vaclav Kotesovec, Oct 20 2014

(* N[Sum[Tan[1/n]^2, {n, 1, Infinity}], 120], yields only 25 correct decimals *)

default(realprecision,120); sumpos(n=1,(tan(1/n))^2) \\ Vaclav Kotesovec, Oct 20 2014

A248951 Decimal expansion of sum_{n >= 1} (tan(2/n))^2.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Oct 18 2014

			9.0435286086582111526563827472958995791513335719871504139242512780719363...

Vaclav Kotesovec, Table of n, a(n) for n = 1..500

Cf. A248946, A248947, A248948, A248950.

evalf(sum((tan(2/n))^2, n=1..infinity), 120); # Vaclav Kotesovec, Oct 20 2014

(* N[Sum[Tan[2/n]^2, {n, 1, Infinity}], 120], yields only 24 correct decimals *)

default(realprecision,120); sumpos(n=1,(tan(2/n))^2) \\ Vaclav Kotesovec, Oct 20 2014

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

Original entry on oeis.org

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

Bernard Schott, Apr 29 2023

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.

			Equals 0.822082200803588202935870118715993520730...

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

Cf. A096444, A248946, A248948, A342680.

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

sumpos(n=1, tan(1/n) - sin(1/n)) \\ Michel Marcus, Apr 29 2023

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A248947 Decimal expansion of Sum_{n >= 1} tan(1/n)^2.

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A248951 Decimal expansion of sum_{n >= 1} (tan(2/n))^2.

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

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