An infinite geometric series is a series of numbers where each term is multiplied by a constant ratio to get the next term. This series continues infinitely, and can either approach a finite limit or diverge to infinity.
The formula for finding the sum of an infinite geometric series is S = a / (1 - r), where a is the first term and r is the common ratio between terms.
If the absolute value of the common ratio (r) is less than 1, then the series will converge to a finite limit. If the absolute value of r is greater than or equal to 1, then the series will diverge to infinity.
Yes, an infinite geometric series can have a negative common ratio. The series will still converge or diverge based on the absolute value of the ratio.
Infinite geometric series can be used to model exponential growth or decay, such as in population growth, interest rates, and radioactive decay. They can also be used in finance and economics, such as in calculating compound interest.