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A127198
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Value of the Foxtrot sum Sum_{k>=1} (-1)^(k + 1)*k^2/(k^3 + 1).
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0
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2, 3, 9, 5, 6, 0, 7, 4, 7, 3, 4, 0, 7, 4, 1, 9, 4, 9, 8, 7, 8, 1, 5, 3, 2, 5, 1, 1, 3, 8, 0, 3, 4, 1, 5, 1, 4, 8, 0, 1, 0, 8, 6, 2, 3, 9, 9, 3, 3, 6, 9, 4, 0, 8, 6, 0, 1, 1, 9, 6, 3, 5, 9, 3, 9, 6, 7, 3, 1, 4, 1, 5, 5, 3, 8, 2, 3, 1, 2, 8, 1, 6, 9, 8, 2, 6, 4, 6, 8, 4, 6, 1, 0, 6, 3, 2, 2, 7, 3, 5, 6, 6, 5, 8, 1
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OFFSET
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0,1
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COMMENTS
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The calculation of this sum is one of the four questions in the exam given to Paige Fox in the June 2, 1996 comic strip FoxTrot by Bill Amend. - Amiram Eldar, Jun 27 2021
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REFERENCES
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Bill Amend, Camp Foxtrot, Kansas City, MO: Andrews McMeel Publishing, 1998, p. 19.
Bill Amend, The Best of FoxTrot, Kansas City, MO: Andrews McMeel Publishing, 2010, p. 212.
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LINKS
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Margaret Cibes and James Greenwood, Media Clips, The Mathematics Teacher, Vol. 100, No. 5 (2006/2007), pp. 338-342.
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FORMULA
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Equals (1 - log(2) + Pi*sech((sqrt(3)*Pi)/2))/3.
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EXAMPLE
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0.23956074734074194987815325113803415148010862399336...
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MATHEMATICA
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RealDigits[(1 - Log[2] + Pi*Sech[(Sqrt[3]*Pi)/2])/3, 10, 100][[1]]
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PROG
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(PARI) sumalt(k=1, (-1)^(k + 1)*k^2/(k^3 + 1)) \\ Michel Marcus, Jun 27 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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