The "Foxtrot series" is a mathematical sum that appeared in the June 2, 1996 comic strip FoxTrot by Bill Amend (Amend 1998, p. 19; Mitchell 2006/2007). It arose from a convergence testing problem in a calculus book by Anton, but was inadvertently converted into a summation problem on an alleged final exam by the strip's author:
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(1)
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The sum can be done using partial fraction decomposition to obtain
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(2)
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 |  | ![1/3(1-ln2)+(zeta^2)/3sum_(n=1)^(infty)(-1)^n(1-2n)×[1/((1+zeta)(zeta-n))+1/((1+zeta)(zeta^2+n))]](/images/equations/FoxTrotSeries/Inline6.svg) |
(3)
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 |  | ![1/3[1-ln2+pisech(1/2sqrt(3)pi)]](/images/equations/FoxTrotSeries/Inline9.svg) |
(4)
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(5)
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(OEIS A127198), where 
and the last sums have been done
in terms of the digamma function and symbolically
simplified.
