Question: How to calculate difference of two sums algebraically?

Dear Maple Users

I wonder if and how I can use Maple to calculate the difference of two sums algebraically, meaning if I dont have an explicit expression for the range of the sum. Rather, I want to calculate

Sum(i, i=0..N) - Sum(i, i=0..N, i!=k);

which should, obviously return k.

Is it possible to evaluate such an expression, and more advanced cases, using Maple?
Thanks for hints.


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