meeklobraca said:
meeklobraca said:
tiny-tim said::rofl: :rofl: :rofl: :rofl:
Hint: does it converge for x = 0?
meeklobraca said:
An infinite geometric series is a sequence of numbers where each term is a constant multiple of the previous term. It has an infinite number of terms and can either converge to a specific value or diverge to infinity.
In order for an infinite geometric series to converge, the absolute value of the common ratio (r) between terms must be less than 1. If the absolute value of r is greater than or equal to 1, the series will diverge.
The formula for finding the sum of a convergent infinite geometric series is S = a / (1-r), where S is the sum, a is the first term, and r is the common ratio between terms.
Yes, an infinite geometric series can have a negative common ratio. If the absolute value of the common ratio (r) is less than 1, the series will still converge to a specific value. However, if the absolute value of r is greater than or equal to 1, the series will diverge regardless of whether the common ratio is positive or negative.
Yes, it is possible for an infinite geometric series to converge to a negative value. This can happen if the first term (a) is negative and the absolute value of the common ratio (r) is less than 1. The series will still converge to a negative value, but the absolute value of the sum will be less than the absolute value of the first term.