> On Fri, Nov 8, 2013 at 5:05 PM, Dan Drake <ddrake at math.wisc.edu
> <mailto:ddrake at math.wisc.edu>> wrote:
>
> Hello,
>
> A Sage user encountered a problem that seems to come from Maxima. See
> https://groups.google.com/forum/#!topic/sage-support/dwR4kuBmiQo
> <https://groups.google.com/forum/#%21topic/sage-support/dwR4kuBmiQo>;.
> In
> Sage:
>
> sage: n = var('n')
> sage: assume(n>0)
> sage: series = -(3*n^2 + 1)*(-1)^n/sqrt(n^5 + 8*n^3 + 8)
> sage: limit(series, n=infinity)
> 38/25*pi^2*und
>
> And in Maxima:
>
> (%i6) display2d:false;
>
> (%o6) false
> (%i7) limit(-(3*n^2 + 1)*(-1)^n/sqrt(n^5 + 8*n^3 + 8),n,inf);
>
> (%o7) -38*und*log(-1)^2/25
>
> I would expect Maxima to evaluate the limit and get zero.
> (Possibly with
> some encouragement?)
>
> (I'm not on the mailing list, I'm just reporting a bug -- further
> discussion can be directed to the sage-support mailing list or to our
> trac ticket: http://trac.sagemath.org/ticket/15386.)
>
> Thanks,
>
> Dan
It is easy to prove:
If limit(|x[n]|, n, inf)=0 then limit(x[n], n, inf)=0.
(%i1) limit(abs(-(3*n^2 + 1)*(-1)^n/sqrt(n^5 + 8*n^3 + 8)),n,inf);
(%o1) 0
Then limit(-(3*n^2 + 1)*(-1)^n/sqrt(n^5 + 8*n^3 + 8),n,inf) = 0.
best
Aleksas D