Convergence Test for 1/(sqrt(k+5)) - How to Determine Series Convergence?

In summary, the conversation discusses whether the given series converges and the use of the integral test. The person asking for help is unsure of how to begin and is struggling with taking limits. However, they suggest that the series diverges and mention the possibility of using the harmonic series.
  • #1
raincheck
38
0

Homework Statement


Determine whether the series converges:
1/(sqrt(k+5))


Homework Equations


well i think I'm supposed to use the integral test, which has you take the integral of the series and the limit too..


The Attempt at a Solution


.. I'm just not sure how to begin, for some reason I'm completely BLANKING on how to take limits.. i know that the series diverges, but i don't know how to actually get that answer.
 
Physics news on Phys.org
  • #2
There is also that for all k, [tex]\frac{1}{\sqrt(k+5)}>\frac{1}{k+5}[/tex] and [tex]\sum \frac{1}{k+5}[/tex] is essentially the harmonic series. :rolleyes:

But I don't understand why you say you don't know where to begin while just before you were suggesting the use of the integral test.. :confused:
 
Last edited:

FAQ: Convergence Test for 1/(sqrt(k+5)) - How to Determine Series Convergence?

What is a convergence test problem?

A convergence test problem is a mathematical problem that is used to determine whether a series or sequence of numbers converges or diverges. It is used to evaluate the behavior of a series as the number of terms increases towards infinity.

Why is it important to solve convergence test problems?

Solving convergence test problems is important because it helps us understand the behavior of a series or sequence of numbers. It allows us to determine whether a series converges to a specific value or diverges to infinity, which is crucial in many applications of mathematics and science.

What are some commonly used convergence tests?

Some commonly used convergence tests include the ratio test, the root test, the integral test, and the comparison test. These tests have different criteria for determining convergence or divergence and are used depending on the nature of the series.

How do you know when to use a particular convergence test?

The choice of convergence test depends on the type of series and the information given in the problem. For instance, the ratio test is used for series involving powers of n, while the integral test is used for series involving functions. It is important to carefully analyze the given series before deciding on which convergence test to use.

What are some applications of convergence test problems?

Convergence test problems have various applications in mathematics, physics, engineering, and other fields. For example, they are used in the analysis of algorithms, signal processing, and differential equations. In physics, convergence tests are used to determine the behavior of physical systems, such as the behavior of electric fields and gravitational forces.

Similar threads

Interval of convergence of power series from ratio test
Replies
2
Views
842
Valid conclusion for an absolutely convergent sequence
Replies
4
Views
712
Determining if a series converges
Replies
4
Views
1K
Proving convergence and divergence of series
Replies
3
Views
869
Pointwise convergence for all real x
Replies
5
Views
477
Special Comparison Test For Infinite Series
Replies
4
Views
630
Test the following series for convergence or divergence
Replies
7
Views
2K
Ratio Test vs AST
Replies
4
Views
650
Does the Alternating Series Test show convergence for this series?
Replies
14
Views
2K
Does the series converge using the integral test?
Replies
16
Views
3K

Hot Threads

Recent Insights

Back
Top