OFFSET
0,1
COMMENTS
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
REFERENCES
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.
LINKS
Richard Askey, The "Foxtrot" sum: Homage to Euler on the 300th anniversary of his birth, The Mathematics Teacher, Vol. 101, No. 6 (2008), pp. 404-406.
Margaret Cibes and James Greenwood, Media Clips, The Mathematics Teacher, Vol. 100, No. 5 (2006/2007), pp. 338-342.
Eric Weisstein's World of Mathematics, Foxtrot Series.
FORMULA
Equals (1 - log(2) + Pi*sech((sqrt(3)*Pi)/2))/3.
EXAMPLE
0.23956074734074194987815325113803415148010862399336...
MATHEMATICA
RealDigits[(1 - Log[2] + Pi*Sech[(Sqrt[3]*Pi)/2])/3, 10, 100][[1]]
PROG
(PARI) sumalt(k=1, (-1)^(k + 1)*k^2/(k^3 + 1)) \\ Michel Marcus, Jun 27 2021
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Jan 08 2007
STATUS
approved