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#2045 Error in symbolic summation
As reported in the thread http://groups.google.com/group/sage-devel/browse_thread/thread/019f1fb75bf4a07f/4aabfec7592d8c96?show_docid=4aabfec7592d8c96# and confirmed as a bug by Robert Dodier, there seems to be a bug in simplify_sum.
(%i1) load(simplify_sum);
<snip>
(%i3) simplify_sum(sum(binomial(n,k)*binomial(k-1,j)*(-1)**(k-1-j),k,j
+1,n));
(%o3) 0
(%i4) simplify_sum(sum(binomial(5,k)*binomial(k-1,3)*(-1)**(k-1-3),k,
4,5));
(%o4) 1
(%i5) 5*1*1+1*4*(-1);
(%o5) 1
Fixed in git:
(%i4) simplify_sum(sum(binomial(n,k)*binomial(k-1,j)*(-1)^(k-1-j),k,j+1,n));
Is j+1 positive, negative, or zero?
pos;
(%o4) 1