Answer
1
Work Step by Step
To solve the given problem, we must first identify what it is asking. By asking what $S_\infty$ of the sequence is, it is asking what the sum of the sequence converges to after infinite terms. We see that the sign alternates for each term in the sequence, and the denominator of the fraction is always 3. The denominator of the sequence is double of the denominator of the term before. Adding terms until we see what the sequence converges to, we find:
$$ \frac{3}{2} + -\frac{3}{4} + \frac{3}{8} + -\frac{3}{16} + \frac{3}{32}+ ... + a_\infty \\ =1 $$
