salbakuta03 said:Homework Statement
Show [tex]\sum_{k=1}^{\infty} c\k^(1\div2k)[/tex], c is an element of [tex]\Re[/tex], c > 0, is divergent.
Homework Equations
1/n is divergent
The Attempt at a Solution
Finding a similar series and doing comparison test, is it right?
When a series is divergent, it means that the terms of the series do not approach a finite limit as the number of terms increases. In other words, the sum of the terms of the series does not have a definite value.
To show that a series is divergent, you can use one of several tests such as the divergence test, integral test, or comparison test. These tests involve evaluating the limit of the series or comparing it to a known divergent series.
No, a series cannot be both convergent and divergent. A series can only have one of these two classifications, depending on whether or not the terms approach a finite limit as the number of terms increases.
There is no one specific method for determining if a series is divergent. However, there are several tests that can be used to evaluate the convergence or divergence of a series depending on its form.
Showing that a series is divergent can be important in various mathematical calculations and applications. It can also help determine the behavior of a series and provide insight into the underlying patterns and relationships within the series.