I'm very sorry. The answer to my questions were all found in your posting. I sent my last posting before properly comprehending your last example.
Thanks for the help.
Thanks for your post describing the distinction between add/sum. However, I'm working with a large number of functions with conditional definitions, and I'm trying to find closed forms for summations of various expressions built from them, so I really do need the sum function, not the add function.
Consider my first example:
From your post, I see why it doesn't work (although I still think it would be helpful for Maple to generate a warning that the k doesn't have a value defined). Hence, this answers the first question raised by my post -> no, this behaviour isn't a bug.
But, it doesn't answer my other question: is there another way to use Maple to solve for closed forms of conditional expressions where the condition is parameterized by the summation index? Obviously my second example:
n + sum(binomial(n,k),k=1..n)
was created by manually splitting up the summation range and substituting the appropriate expressions. I can therefore use this approach to solve my problems, but it is tedious since I have several levels of nested summations and the number of cases multiplies quickly.
Any ideas if there is a better way?