Final answer:
The given geometric series with a first term of 8.7 and a common ratio of 0.4 converges because the absolute value of the common ratio is less than 1.
Step-by-step explanation:
To determine whether the given geometric series converges or diverges, we need to identify the first term and the common ratio (r), and then apply the convergence criteria for geometric series.
The first term of the series is 8.7, and by looking at subsequent terms, we can see that each term is obtained by multiplying the previous term by 0.4 (since \(3.48 = 8.7 \times 0.4\), \(1.392 = 3.48 \times 0.4\), and so on). Therefore, the series is a geometric series with a common ratio of 0.4.
A geometric series converges if the absolute value of the common ratio is less than 1 (\(|r| < 1\)). Since the common ratio here is 0.4, which is less than 1, the given geometric series converges.