why is it an error to try to find a divergent sum? If a sum is positive and
unbounded, wouldn't it be inf?
if a sum is positive and unbounded, why not return inf?
I tried Mathematica 6.0, and it gives error messages, but I don't see why
that is a good idea, if you can actually compute with symbols like inf.
(which, arguably, we can't :) )
RJF
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu
> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of Andrej Vodopivec
> Sent: Tuesday, April 22, 2008 3:12 AM
> To: Maxima - list
> Subject: Divergent sums
>
> Hi,
>
> I looked a little into the bug 1945954 (simpsum/simplify_sum with
> summand=f(i)+q) and noticed that there are many bugs with divergent
> sums:
>
> (%i2) simpsum:true$
> (%i3) sum(2^n-3^n,n,1,inf);
> (%o3) inf
> (%i4) sum(3^n-2^n,n,1,inf);
> (%o4) minf
> (%i5) sum((-3)^n,n,1,inf);
> (%o5) minf
>
> Basically, if the sum is divergent, maxima answers inf, minf or und,
> but a lot of times incorrectly.
>
> I propose to change that so that for divergent sums maxima returns und
> or signals an error. This would make sum behave more like integrate:
>
> (%i8) integrate(1/x,x,1,inf);
> Integral is divergent
> -- an error. To debug this try debugmode(true);
>
> and remove some bugs.
>
> --
> Andrej
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