A343470 Decimal expansion of Sum_{n>=1} ((-1)^(n-1))*arctan(n)/n.

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

Offset

0,1

Comments

The alternating series test shows the series is convergent.

Links

Table of n, a(n) for n=0..91.

Wikipedia, Alternating series test.

Formula

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

Example

0.46571230352630363552682770124023013687237216061516248...

Maple

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

Prog

(PARI) sumalt(n=1, (-1)^(n-1)*atan(n)/n) \\ Michel Marcus, Apr 17 2021

Crossrefs

Cf. A343469, A265011.

Sequence in context: A243396 A140243 A366872 * A199289 A306341 A306654

Adjacent sequences: A343467 A343468 A343469 * A343471 A343472 A343473

Keyword

nonn,cons

Author

Bernard Schott, Apr 17 2021

Status

approved