# How do you determine if the series the converges conditionally, absolutely or diverges given #Sigma ((-1)^(n))/(sqrt(n+4))# from #[1,oo)#?

##### 1 Answer

The series:

is convergent but not absolutely convergent.

#### Explanation:

This is an alternating series in the form:

thus based on Leibniz's theorem, it is convergent if:

In our case:

and

so both conditions are satisfied and the series is convergent.

Consider now the series of absolute values:

Using the limit comparison test we can see that as:

the series

which is divergent based on the

The series

is convergent but not absolutely convergent.