Question about independance WRT sums



When experimenting with sums, I came across the following series
of results:


(C1) simpsum:true;

(D1) 				     TRUE
(C2) sum(i, i, 1, n);

				     2
				    n  + n
(D2) 				    ------
				      2
(C3) sum( 2 . i, i, 1, n);

				     2
(D3) 				    n  + n
(C4) sum( k. i, i, 1, n);

				  n
				 ====
				 \
(D4) 				  >    (k . i)
				 /
				 ====
				 i = 1


I first expected Maxima to come back with k( n^2 + n) / 2 or
some equivalent form.

I assume that Maxima isn't making the simplification because
it doesn't make the assumption that k is indpendant of
Is my interpretation accurate?  If so, is there some way I can tell maxima
that k is indeed independant of i and have it make the appropriate
simplification?

Would it make more sense to assume independence by default? Mathematica
did in the same situation IIRC.


-- 
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Robert Merkel	                           rgmerk@mira.net

Go You Big Red Fire Engine
-- Unknown Audience Member at Adam Hills standup gig
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