Absolute convergence of series

[Kqwert]

Homework Statement

Hello, I need some feedback on whether this reasons is correct.

consider the series

Examine the series for absolute convergence.

Homework Equations

The Attempt at a Solution

How I have solved this, using the limit comparison test:

we have:

introducing

we have that

We know that bn diverges (harmonic series) , and we can therefore conclude that also an diverges. True?

 

[LCKurtz]

Yes. That is correct.

 

[Mark44]

@Kqwert, instead of posting a bunch of image attachments, why don't you take 5 minutes and look at our LaTeX tutorial (https://www.physicsforums.com/help/latexhelp/)?
The first summation in your post is $\sum_{n = 1}^\infty \frac{(-1)^{n + 1}}{n + \ln(n)}$

The MathJax markup I used above is $\sum_{n = 1}^\infty \frac{(-1)^{n + 1}{n + \ln(n)}$