Final answer:
The sum of the infinite series ∑n=1an with partial sums Sn = 2 - 3(0.8)n is found by removing the diminishing term 3(0.8)n as n approaches infinity, leaving the sum to be 2. The correct answer is b)
Step-by-step explanation:
To calculate the sum of the series represented by Sn = 2 - 3(0.8)n, we need to consider the behavior of the series as n approaches infinity. The sum of an infinite series ∑n=1an is the limit of the partial sums Sn as n goes to infinity, if that limit exists.
In this case, we consider the term 3(0.8)n as n grows larger and larger. Since 0.8 is less than 1, (0.8)n gets closer to zero as n increases. Thus, in the limit as n approaches infinity, this term will converge to 0.
The sum of the series is then simply the remaining term after the 3(0.8)n term has been removed. That is, the sum of the series is the constant term 2 as it is not affected by n.
The sum of the series ∑n=1an is 2. The term that diminishes as n approaches infinity does not contribute to the sum of the series.