A343469 Decimal expansion of Sum_{n>=1} (-1)^(n-1)/(n*arctan(n)).

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

Offset: 0

Author

Bernard Schott, Apr 16 2021

Keywords

• nonn
• cons

Comments

The alternating series test shows this series is convergent.

Examples

			0.98085427459135061539223227829901962211854180072023203606979...
		

Links

• Wikipedia, Alternating series test.

Crossrefs

Cf. A343470, A265011.

Programs

Maple

evalf(sum((-1)^(n-1)/(n*arctan(n)), n=1..infinity),120);

PARI

sumalt(n=1, (-1)^(n-1)/(n*atan(n))) \\ Michel Marcus, Apr 16 2021

Formula

Equals Sum_{n>=1} (-1)^(n-1)/(n*arctan(n)).