Sum of an Infinite Geometric Series
Big Question: Can you add up infinitely many numbers and get a finite answer? Surprisingly, yes — but only under certain conditions!
📌 Quick Review: What is a Geometric Series?
A geometric series is the sum of terms in a geometric sequence, where each term is obtained by multiplying the previous term by a constant ratio $r$.
A finite geometric series with $n$ terms looks like:
$$ S_n = a + ar + ar^2 + ar^3 + \cdots + ar^{n-1} = a \cdot \frac{1 - r^n}{1 - r} $$