Ratio Test =) said:Its a riemann sum.
Convergence is a term used in mathematics to describe a sequence or series that approaches a specific value or limit as the number of terms increases. In other words, the terms of the series get closer and closer to a certain value, but may never actually reach it.
There are several tests that can be used to determine if a series will converge, including the ratio test, the root test, and the comparison test. These tests involve checking the behavior of the terms in the series as the number of terms increases, and can help determine if the series will approach a finite value or diverge to infinity.
No, a series can only converge to one value. If a series has multiple possible values, it is considered to be divergent.
In some cases, it is possible to manipulate a divergent series in order to make it converge. This is often done through the process of summation, which involves grouping terms in a series in a certain way to create a convergent series.
Determining if a series converges is important in many areas of mathematics and science. It allows us to understand the behavior of functions and equations, and helps us make predictions and calculations about various phenomena. In addition, knowing if a series converges can also provide insight into the underlying properties and patterns of a given system or problem.