[Maxima-bugs] [maxima:bugs] #4634 Divergent integral simplifies to -1/4 with simplify_sum

[Barton W. <wil...@us...>]

With Maxima 5.48.1, we're back to the* incorrect* value of `ind`

~~~
(%i11)	simplify_sum(sum(n*(-1)^n,n,1,inf));
(%o11)	ind
~~~

This result is wrong and it is due to a bug in the limit 

~~~
(%i12)	simplify_sum(sum(n*(-1)^n,n,1,N));
(%o12)	((-1)^N*(2*N+1))/4-1/4

(%i13)	limit(%,N,inf);
(%o13)	ind
~~~
The output `%o12` is correct, but the  output `%o13` should be `und`, not `ind`.

Thanks for this reporting this bug.




---

**[bugs:#4634] Divergent integral simplifies to -1/4 with simplify_sum**

**Status:** open
**Group:** None
**Created:** Tue Nov 18, 2025 12:58 PM UTC by kcrisman
**Last Updated:** Tue Nov 18, 2025 12:58 PM UTC
**Owner:** nobody


In the [Sage support list](https://groups.google.com/g/sage-support/c/pCYoD6x2Y8M) we have the following message about a divergent integral giving a solution with the optional package `simplify_sum`.

"In maxima 5.47.0 I get:

```
(%i1) load(simplify_sum)$
(%i2) simplify_sum( sum(n*(-1)^n,n,1,inf));
-1/4
```

This happens both on sage's ECL based one and on the system maxima (running on SBCL). "

That this is a reversion is seen from the following:

```
Maxima 5.42.2 http://maxima.sourceforge.net
using Lisp ECL 16.1.2
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.
(%i1) load(simplify_sum)$

(%i2) simplify_sum( sum(n*(-1)^n,n,1,inf));
(%o2)                                 ind
```



---

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