A wrong (easy) limit

[jvarona]

If we define f(n)=2+1/factorial(n) the answer of sage for limit(1/f(n),n=oo) is 1, that is clearly wrong. However, limit(f(n),n=oo) gives the answer 2, that is correct.

I have seen this problem in (at least) sage 4.6 and sage 4.6.2, in several kind of computers.

[kcrisman]

This is in Maxima.

sage: maxima_console()
;;; Loading #P"/Applications/MathApps/sage/local/lib/ecl/SB-BSD-SOCKETS.fas"
;;; Loading #P"/Applications/MathApps/sage/local/lib/ecl/SOCKETS.fas"
;;; Loading #P"/Applications/MathApps/sage/local/lib/ecl/DEFSYSTEM.fas"
;;; Loading #P"/Applications/MathApps/sage/local/lib/ecl/cmp.fas"
;;; Loading #P"/Applications/MathApps/sage/local/lib/ecl/sysfun.lsp"
Maxima 5.22.1 http://maxima.sourceforge.net
using Lisp ECL 10.4.1
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i3) limit(2+1/factorial(n),n,inf);
(%o3)                                  2
(%i4) limit(1/(2+1/factorial(n)),n,inf);
(%o4)                                  1

This is still present in the latest Maxima. See  this report.

[kcrisman]

 This report suggests it is fixed in the latest upstream. This would need a patch to verify, once we would update Maxima to that release.

[mjo]

This is fixed in stable maxima 5.24.0:

sage: f(n)=2+1/factorial(n)
sage: limit(1/f(n),n=oo)
1/2
sage: limit(f(n),n=oo)
2
sage: maxima.version()
'5.24.0'

[mjo]

Add a doctest for this result. Apply on top of #11483 and #11591 to avoid fuzz.

[mjo]

Maxima 5.24 has a positive review now, so here's a doctest. The file maxima_lib.py gets some new doctests in #11483 and #11591 so to avoid fuzz, apply on top of those (we don't require either of them for the result, though).