Need help on this series test for convergence or divergence

In summary, The equation given is a summation from n=1 to infinity of [(-1)^n] / [sqrt(2n+3)]. The attempt at a solution involved comparing it to 1/sqrt(2n) and using the limit comparison test, but this method does not work in this case. The conversation also mentions other criteria such as Abels, Dirichlets, and Leibniz, but the person has not heard of them. They have also tried using the limit comparison test on sqrt(2n)/sqrt(2n+3), but this does not prove that both series are divergent.
  • #1
rodneyram
3
0

Homework Statement



The equation is the summation from n=1 to infinity of [(-1)^n] / [sqrt(2n+3)].

Homework Equations



If the series An is compared to a a series Bn that diverges and the series An is greater than the series Bn they both diverge.

If the limit from n to infinity of An/Bn is greater than 1, they both converge or diverge.

The Attempt at a Solution



Can I compare this to 1/sqrt(2n), which is greater than the main problem, and then use the limit comparison test to conclude that the series diverges?

Is this correct?
 
Physics news on Phys.org
  • #2
rodneyram said:

Can I compare this to 1/sqrt(2n), which is greater than the main problem, and then use the limit comparison test to conclude that the series diverges?
Is this correct?


It wouldn't work in this case. The series 1/sqrt(2n) is greater then the main problem, but diverges. This doesn't mean that the smaller series has to diverge. In fact, I think that the series in your problem converges.

Have you heard of one of the following: Abels criterion, Dirichlets criterion, Leibniz criterion?
 
  • #3
No, I haven't heard of any of those.

I used the limit comparison test on the two series sqrt(2n)/sqrt(2n+3) which equals to one. Doesn't that prove they are both divergent because the limit is greater than 0 due to the limit comparison test?
 

FAQ: Need help on this series test for convergence or divergence

What is a series test for convergence or divergence?

A series test is a method used to determine whether an infinite series, or a sum of infinitely many terms, converges (approaches a finite value) or diverges (does not approach a finite value) to infinity. It involves evaluating the behavior of the terms in the series to determine its convergence or divergence.

Why is it important to test for convergence or divergence?

It is important to test for convergence or divergence because it allows us to determine whether an infinite series actually has a finite sum or not. This information is crucial in applications where the sum of a series is needed, such as in physics and engineering calculations.

What are some common series tests for convergence or divergence?

Some common series tests include the integral test, comparison test, ratio test, root test, and alternating series test. These tests all have different criteria and are used for different types of series.

How do you know which series test to use?

The choice of series test depends on the behavior of the series and the type of terms involved. Generally, it is helpful to start with the ratio or root test, and then move on to other tests if needed. It is also important to check for any special cases, such as alternating series, which may require a specific test.

What should I do if a series does not converge or diverge using any of the common tests?

If a series does not converge or diverge using any of the common tests, it may be necessary to use more advanced techniques, such as the limit comparison test or the alternating series test with error bounds. If all else fails, it may be necessary to use numerical methods to approximate the sum of the series.

Similar threads

Proving convergence and divergence of series
Replies
3
Views
851
Interval of convergence of power series from ratio test
Replies
2
Views
822
Is Using the Comparison Test to Prove Divergence Valid for This Series?
Replies
29
Views
2K
Valid conclusion for an absolutely convergent sequence
Replies
4
Views
694
Determining if a series converges
Replies
4
Views
1K
Root test proof using Law of Algebra
Replies
6
Views
1K
Absolute convergence of series
Replies
2
Views
995
Proving the convergence of series
Replies
14
Views
2K
Does the Alternating Series Test show convergence for this series?
Replies
14
Views
2K
Why the series is divergent based on the Preliminary test
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top