Answer
The sum of the series $\Sigma a_{n} $ (where n is an integer starting at 1 and approaching infinity) $\infty$) is :
$\lim\limits_{n \to \infty} s_{n}$ -- $\lim\limits_{n \to \infty} ( 2-3 (.8)^{n}$ ) -- $2-3 \lim\limits_{n \to \infty}.8^{n}$ , the final limit is equal to zero
and the answer is 2.
Work Step by Step
Using Definition 2 in page 748, finding the the sum of the series $\Sigma a_{n} $ (where n is an integer starting at 1 and approaching infinity) requires taking the limit of the provided nth partial sum as n approaches infinity. The limit of the partial sum exists and its result is the sum of the series. The result is 2 since the the term that is related to n goes to zero). Notice that we used the series notation properties from Theorem 8 property ii , page 754.
