A353231 Decimal expansion of Sum_{k>=1} (-1)^(k+1) / k^(1+1/k).

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

Offset

0,1

Comments

This series is convergent according to the alternating series test.

References

J.-M. Monier, Analyse, Tome 3, 2ème année, MP.PSI.PC.PT, Dunod, 1997, Exercice 3.3.9.a p. 266.

Links

Table of n, a(n) for n=0..98.

Mark J. Cooker, Fast formulas for slowly convergent alternating series, The Mathematical Gazette, Vol. 95, No. 533 (2011), pp. 218-226; Correspondence, ibid., pp. 560-561 (erratum).

Formula

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

Example

0.7795115373932815692840107386888575715...

Maple

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

Mathematica

RealDigits[NSum[(-1)^(k+1)/k^((k+1)/k), {k, 1, Infinity}, WorkingPrecision -> 120, Method -> "AlternatingSigns"], 10, 105][[1]] (* Amiram Eldar, Jan 02 2023 *)

Prog

(PARI) sumalt(k=1, (-1)^(k+1) / k^(1+1/k)) \\ Michel Marcus, May 02 2022

Crossrefs

Cf. A002162 (Sum_{k>=1} (-1)^(k+1)/k).

Sequence in context: A157290 A021566 A361010 * A335847 A244649 A267040

Adjacent sequences: A353228 A353229 A353230 * A353232 A353233 A353234

Keyword

nonn,cons

Author

Bernard Schott, May 01 2022

Status

approved