Is there a "Sum of range" concept in Math and if so what does it stands for?

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I am not a mathematician but I've came across the concept "sum of range" in the past → I don't recall where exactly.

I didn't find a relevant Wiki article, nor some basic conceptual data on this in a quick search or some statistics introduction books I have read.

Is there a "Sum of range" concept in Math and if so what does it stands for?
That is to ask; is this an existing formal math concept and if so, what main problem or problems it is used to solve?