It is a bug in Maxima (I also checked with Maxima compiled with SBCL, another lisp compiler, more popular than ECL we use). I think it does not pay attention to the 0th term being negative. Indeed, if you sum from 1, not from 0, it correctly outputs (2 log(2)+1)/3.
Dima On Wednesday, November 2, 2016 at 7:09:13 PM UTC, John H Palmieri wrote: > > Sage is not computing a particular infinite sum correctly. > > sage: sum(1/((n+1)*(2*n-1)), n, 0, 1000).n() > -0.205068171626375 > sage: sum(1/((n+1)*(2*n-1)), n, 0, 10000).n() > -0.204618542543703 > sage: sum(1/((n+1)*(2*n-1)), n, 0, 100000).n() # seems to be converging > -0.204573546255870 > sage: sum(1/((n+1)*(2*n-1)), n, 0, oo).n() # but not to this number > -1.09345743518226 > > sage: sum(1/((n+1)*(2*n-1)), n, 0, oo) > 2/3*log(2) - 14/9 > > I think the answer should be 2/3*log(2) - 2/3 -- that's what Mathematica > says, and it is also consistent with the partial sums. (See > https://ask.sagemath.org/question/35354/sage-seems-to-be-improperly-computing-an-infinite-sum-and-giving-an-incorrect-answer/.) > > Is this a bug in Maxima? I don't know enough about Maxima's syntax to > evaluate it directly there. Just for kicks, I also installed "giac", since > that was listed as an option for the "algorithm" keyword for "sum": > > sage: sum(1/((n+1)*(2*n-1)), n, 0, oo, algorithm='giac') > +Infinity > > Not an improvement. > > -- > John > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
