Does the series \[ -\frac{8}{3}+\frac{16}{9}-\frac{32}{27}+\cdots \] converge? If so, find the sum. Converges to: Diverges

Step 1 ：Identify the series as a geometric series, where each term is multiplied by a constant to get the next term.

Step 2 ：Determine the common ratio of the series. In this case, the common ratio is -2/3.

Step 3 ：Check if the series converges. A geometric series converges if the absolute value of the common ratio is less than 1. Here, the absolute value of the common ratio is less than 1, so the series does converge.

Step 4 ：Calculate the sum of the series using the formula for the sum of an infinite geometric series, which is \(a / (1 - r)\), where \(a\) is the first term and \(r\) is the common ratio. In this case, \(a = -8/3\) and \(r = -2/3\).

Step 5 ：Substitute the values of \(a\) and \(r\) into the formula to get the sum of the series. The sum of the series is \(-1.6\).

Step 6 ：Final Answer: The series converges to \(\boxed{-1.6}\).