Convergent Series: Introduction & Identification

In summary, a convergent series is one that converges to a finite value, and there are various tests to determine if a given series is convergent. These include the "number of terms" test and the "limit" test.
  • #1
hsaimul
1
0
I need to know about converge series.For example how to identify a converge series.Plz explain.
 
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  • #2
hsaimul said:
I need to know about converge series.For example how to identify a converge series.Plz explain.



This is not a consult question. You need either to take a course in basic analysis, or read a book or, at least, check google under "infinite series".

DonAntonio
 
  • #3
Get Spivaks Calculus and work through it.
 
  • #4
A convergent series is a series that converges to a finite value. There are several tests to find if a given series is convergent. First, there's the "number of terms" test. If your series has a finite number of terms, it's convergent. Easily done. There's also the "limit" test. If the terms in your series don't tend to zero, it's not convergent.

There are other tests that can help you out here, but I don't feel like enumerating all of them.
 

1. What is a convergent series?

A convergent series is a mathematical series in which the sum of all its terms approaches a finite number as more terms are added. This means that the series has a limit and does not continue to grow indefinitely.

2. How can I identify if a series is convergent?

There are several tests that can be used to determine if a series is convergent. Some common tests include the comparison test, the ratio test, and the integral test. These tests involve evaluating certain properties of the series, such as the behavior of the terms or the convergence of an integral, to determine if the series is convergent.

3. What is the difference between a convergent and a divergent series?

A divergent series is one in which the sum of all its terms does not approach a finite number as more terms are added. Instead, the series either grows without bound or oscillates between positive and negative values. This is in contrast to a convergent series, which has a finite limit as more terms are added.

4. Why is it important to study convergent series?

Convergent series are an important part of mathematics and have many real-world applications. They are used to model various phenomena in science and engineering, as well as in statistics and finance. Additionally, understanding convergent series is essential for more advanced mathematical concepts and theories.

5. Can a series be both convergent and divergent?

No, a series cannot be both convergent and divergent. By definition, a series is either convergent or divergent. However, there are cases where a series may be conditionally convergent, meaning that it is convergent but not absolutely convergent. In these cases, the series may appear to be both convergent and divergent, but it is actually just convergent under certain conditions.

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