A geometric series is a sequence of numbers where each term is found by multiplying the previous term by a constant number. It follows the formula a, ar, ar^2, ar^3, ... where 'a' is the first term and 'r' is the common ratio.
The formula for finding the sum of a geometric series is S = a(1 - r^n) / (1 - r), where 'S' is the sum, 'a' is the first term, 'r' is the common ratio, and 'n' is the number of terms.
A finite geometric series has a limited number of terms, while an infinite geometric series continues infinitely. The sum of a finite geometric series can be calculated using the formula mentioned in question 2, while the sum of an infinite geometric series only exists if the common ratio is less than 1.
Geometric series are used in various fields such as finance, physics, and computer science. In finance, it is used to calculate compound interest. In physics, it is used to model the growth or decay of a variable over time. In computer science, it is used in algorithms and data structures.
A geometric series is a sum of a geometric progression. Geometric progression refers to the sequence of numbers, while geometric series refers to the sum of those numbers. In other words, a geometric series is the total of all the terms in a geometric progression.