Final answer:
The infinite geometric series with a first term of -6 and a common ratio of 1/2 has a finite sum of -12, calculated using the formula for the sum of an infinite geometric series: S = a / (1 - r).
Step-by-step explanation:
The question pertains to the concept of geometric series in mathematics. An infinite geometric series with a first term (a) of -6 and a common ratio (r) of (1)/(2) implies an infinite sum of terms where each term is half of the previous term. Since the absolute value of the common ratio is less than 1, this series has a finite sum, which can be found using the formula for the sum of an infinite geometric series: S = a / (1 - r).
To calculate the finite answer for the given series:
- Substitute the first term (-6) into the formula for a.
- Substitute the common ratio ((1)/(2)) into the formula for r.
- Perform the division to find the sum: S = -6 / (1 - (1/2)) = -6 / (1/2) = -12.
Therefore, the infinite series with these given values converges to -12.