On Wednesday, April 16, 2014 8:58:34 AM UTC-4, Alberto Verga wrote:
>
> OK, but why we need to use "limit" to compute a convergent sum...?
> For instance
> sum(1/n^2,n,2,oo)
> gives pi^2/6-1
>
> but
> limit(sum(1/n^2,n,2,x), x=oo)
> do not give a result...
>
>>
>>
This is interesting. In Sage's Maxima:
(%i1) load(simplify_sum);
(%i9) simplify_sum(sum(1/x^2,x,2,inf));
2
%pi
(%o9) ---- - 1
6
(%i10) sum(log(1-1/x^2),x,2,inf);
inf
====
\ 1
(%o10) > log(1 - --)
/ 2
==== x
x = 2
(%i11) simplify_sum(sum(log(1-1/x^2),x,2,inf));
inf + 2
(%o11) log(-----------)
2 (inf + 1)
Which I agree is not a great answer. Using simpsum does the same thing.
I'm not sure if this is expected behavior in Maxima, though?
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