Final answer:
The series -5 + 25 - 125 + ... is a geometric series with a common ratio of -5. Since the absolute value of this common ratio is greater than 1, the series is divergent.
Step-by-step explanation:
The series -5 + 25 - 125 + ... is a geometric series where each term is multiplied by -5 to get the next term. To determine if this series is convergent or divergent, we can use the formula for the sum of a geometric series which is S = a / (1 - r), where a is the first term and r is the common ratio. For a geometric series to converge, the absolute value of r has to be less than 1. In this case, the common ratio r is -5. Since the absolute value of -5 is not less than 1, it means that the absolute value of r is greater than 1, and therefore the series does not converge to a finite number. Hence, the series -5 + 25 - 125 + ... is divergent.