Question

The infinite series with a first term of -6 and a common ratio of (1)/(2) has a finite answer.

Answer 1

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:

1. Substitute the first term (-6) into the formula for a.
2. Substitute the common ratio ((1)/(2)) into the formula for r.
3. 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.