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 A113024 Decimal expansion of Sum_{k>=1} -(-1)^k/sqrt(k). 5
 6, 0, 4, 8, 9, 8, 6, 4, 3, 4, 2, 1, 6, 3, 0, 3, 7, 0, 2, 4, 7, 2, 6, 5, 9, 1, 4, 2, 3, 5, 9, 5, 5, 4, 9, 9, 7, 5, 9, 7, 6, 2, 5, 4, 5, 1, 3, 0, 2, 4, 7, 3, 8, 0, 3, 7, 8, 5, 4, 6, 6, 4, 8, 0, 8, 2, 1, 8, 7, 2, 5, 3, 4, 9, 5, 0, 6, 0, 3, 5, 7, 3, 2, 7, 4, 0, 3, 9, 5, 6, 9, 1, 8, 3, 4, 9, 5, 5, 4, 3, 8, 3, 0, 3, 3 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES Stephen Fletcher Hewson, A Mathematical Bridge: An Intuitive Journey In Higher Mathematics, World Scientific, NJ, 2003, p. 83. LINKS G. C. Greubel, Table of n, a(n) for n = 0..10000 Rick Kreminski, Using Simpson's rule to approximate sums of infinite series, Coll. Math. J. 28 (5) (1997), p 368-376,  Table 1. Eric Weisstein's World of Mathematics, Zeta Function.. FORMULA Equals (1-sqrt(2))*Zeta(1/2) = (-1+A002193) * A059750. A265162/A113024 = gamma/2 + Pi/4 - (1/2 + sqrt(2))*log(2) + log(Pi)/2, where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Dec 03 2015 EXAMPLE 1 - 1/sqrt(2) + 1/sqrt(3) - 1/sqrt(4) + 1/sqrt(5) - 1/sqrt(6) + 1/sqrt(7) ... = 0.60489864342163037024726591423595549975976254513024738037854664808... MATHEMATICA RealDigits[(1 - Sqrt[2])Zeta[1/2], 10, 111][[1]] PROG (PARI) (1-sqrt(2))*zeta(1/2) \\ G. C. Greubel, Apr 09 2018 CROSSREFS Cf. A002193, A059750, A263192, A263193, A265162. Sequence in context: A197148 A196623 A265275 * A112280 A204850 A202394 Adjacent sequences:  A113021 A113022 A113023 * A113025 A113026 A113027 KEYWORD cons,nonn AUTHOR Robert G. Wilson v, Oct 11 2005 STATUS approved

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Last modified August 18 17:55 EDT 2018. Contains 313834 sequences. (Running on oeis4.)