Gib Z said:lol what did I do >.< I can't tell if that's derogatory or a compliment..
Gib Z said:lol but as a whole? Did I say something mean? If so I am sorry >.<
An infinite series is a sum of an infinite number of terms. The terms in an infinite series can be numbers, variables, or more complex expressions, and the series is said to converge if the sum of its terms approaches a finite value as the number of terms increases.
Infinite series are used in calculus to represent functions as a sum of infinitely many terms. This allows for the analysis and manipulation of functions that would otherwise be difficult to work with. Infinite series are also used to approximate values of functions, which is particularly useful in real-world applications.
The main difference between an infinite series and a finite series is the number of terms. A finite series has a limited, finite number of terms, while an infinite series has an infinite number of terms. Additionally, a finite series will have a specific sum, while an infinite series may or may not converge to a finite value.
There are various methods for determining the convergence or divergence of an infinite series, including the comparison test, the integral test, and the ratio and root tests. These methods involve evaluating the behavior of the terms in the series and determining if they approach a finite value or increase without bound.
Infinite series have a wide range of applications in fields such as physics, engineering, and finance. They can be used to model and analyze various phenomena, such as the motion of objects, electrical circuits, and stock market trends. Infinite series also play a crucial role in the development of numerical methods for solving complex problems in these fields.