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A353231
Decimal expansion of Sum_{k>=1} (-1)^(k+1) / k^(1+1/k).
0
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
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
KEYWORD
nonn,cons
AUTHOR
Bernard Schott, May 01 2022
STATUS
approved