Where does the summation formula $(c^n - 1)/(c -1)$ come up? What does it apply to?

Question

A solution I'm looking at employs this formula to find the sum of a finite series, but I haven't been able to find any information on this formula online or in my textbooks. Where does it come from, and what situations does it apply to? (It doesn't seem to be a reorganization of the formula for finite geometric sums...)

Answer 1

It comes from the high-school formula: $$a^n-b^n=(a-b)(a^{n-1}+a^{n-2}b+\dots+ab^{n-2}+b^{n-1})$$ with $a=1$.