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How to extract a variable names (not values) from a list of transformation rules?

I am trying to extract variable names from a list of transformation rules mapping = {var1 -> 'val1', var2 -> 'val2' }. Variables ...
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Need to take infinite sum of residues, is there a way to choose the order of operations for ReleaseHold?

I'm computing an infinite sum of residues. I want to do something like this: ...