Consider that how Sum gives different results when x is set to 1.
In[1]:= Sum[x^-k, {k, 1, n}]
Out[1]= (x^-n (-1 + x^n))/(-1 + x)
In[2]:= x = 1;
Sum[x^-k, {k, 1, n}]
Out[3]= n
Shouldn't Sum have an option to assume if might be be summing a root of unity? Is there a clean and simple way to get this functionality without using variants of Hold and Inactive?
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