 (5)
(OEIS A118582; Mathar 2009) converge by the integral test, although the last converges so gradually that terms are necessary to obtain twodigit accuracy (Zwillinger 1996, p.39). Both can be summed making use of the EulerMaclaurin integration formulas. SEE ALSO: Absolute Convergence, Conditional Convergence, Convergence Tests, Convergent, Convergent Sequence, Divergent Series, Limit, Radius of Convergence, Unidevelop Convergence REFERENCES:Baxley, J.V. "Euler"s Constant, Taylor"s Formula, and also Slowly ConvergingSeries." Math. Mag. 65, 302313, 1992. Braden, B. "Calculating Sums of Infinite Series." Amer. Math. Monthly 99,649655, 1992. Bromwich, T.J.I"A. and MacRobert, T.M. An Summary to the Theory of Infinite Series, 3rd ed. New York: Chelsea, 1991. D"Angelo, J.P. and West, D.B. Mathematical Thinking: ProblemSolving and Proofs, second ed. Upper Saddle River, NJ: PrenticeHall, 2000. Kreminski, R. "Using Simpson"s Rule to Approximate Sums of Infinite Series."College Math. J. 28, 368376, 1997. Mathar, R.J. "The Series Limit of " />." 4 Feb 2009. http://arxiv.org/abs/0902.0789.Sloane, N.J.A. Sequences A115563 and A118582 in "The OnLine Encyclopedia of Integer Sequences." Zwillinger, D. (Ed.). CRC Standard Mathematical Tables and also Formulae, 30th ed. Boca Raton, FL: CRC Press, 1996. Referenced on nlinux.orgAlpha: Convergent Series CITE THIS AS:Weisstein, Eric W. "Convergent Series."From nlinux.orgA nlinux.org Internet Reresource. https://mathpeople.nlinux.org.com/ConvergentSeries.html nlinux.org Net ResourcesMathematica» The #1 tool for producing Demonstrations and anypoint technical.  nlinux.orgAlpha» Explore anypoint with the initially computational knowledge engine.  nlinux.org Demonstrations Project» Explore hundreds of complimentary applications throughout scientific research, mathematics, engineering, technology, service, art, finance, social scientific researches, and even more.  Computerbasedmath.org» Join the initiative for modernizing math education and learning.  Online Integral Calculator» Solve integrals through nlinux.orgAlpha.  Stepbystep Solutions» Walk via homejobrelated troubles stepbyaction from beginning to finish. Hints help you attempt the following step on your very own.  nlinux.org Problem Generator» Limitless random practice difficulties and answers via integrated Stepbystep solutions. Practice virtual or make a printable examine sheet.  nlinux.org Education Portal» Collection of teaching and also learning tools developed by nlinux.org education experts: dynamic textbook, lesboy plans, widgets, interenergetic Demonstrations, and also even more.
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