Final answer:
To find the sum of an infinite geometric series, use the formula S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio, provided |r| < 1.
Step-by-step explanation:
To find the sum of an infinite geometric series, certain conditions must be met. First, the absolute value of the common ratio r must be less than 1. Assuming this is the case, the formula for the sum S of the infinite series is:
S = a / (1 - r)
where a is the first term of the series. Here's how you would apply the formula:
- Determine the first term a of the series.
- Identify the common ratio r between consecutive terms.
- Calculate the sum using the formula S = a / (1 - r).
It's important to remember that this formula only applies when |r| < 1; otherwise, the series does not converge to a sum.