1. Stating the problem: We want to find the sum of a geometric series. 2. Definition: A geometric series is a series of terms where each term is found by multiplying the previous term by a common ratio $r$. The sum of the first $n$ terms is given by the formula $$S_n = a \frac{1-r^n}{1-r}$$ where $a$ is the first term and $r \neq 1$ is the common ratio. 3. Using the formula: Identify $a$, $r$, and $n$ from the given series. 4. Substitute these values into the formula: $$S_n = a \frac{1-r^n}{1-r}$$ 5. Simplify the expression by calculating $r^n$ and then the numerator and denominator. 6. Compute the final sum $S_n$, which gives the total of the first $n$ terms in the geometric series. This method can be applied to any specific geometric series once $a$, $r$, and $n$ are known.