Sum of n Terms of a G.P

We now turn to the central question: if you add the first $n$ terms of a geometric progression, what compact formula captures the total? The answer depends critically on whether the common ratio $r$ is exactly 1 or something else — a small twist that makes all the difference. Understanding this derivation not only gives you a powerful tool for summing growth, decay, and compound-interest problems, but also reveals why the infi …