Series Convergence and Divergence test!

1. The problem statement, all variables and given/known data

So my question was Sum- (n=2) ln(n)/n
2. Relevant equations

I noticed that you can only limit comparison, because so far, I have tried doing all the other test such as the nth term test, p-series, integral(i have no idea how to integrate that).
3. The attempt at a solution

 

Well, it is supposed to diverge? I don't even know what I'm supposed to be comparing it to

 

I tried looking one up, they gave me the answer instead of an explanation or work, and that is the MOST important part.

 

Okay, so you know how to do a limit comparison test we need to compare the function to something right? I'm not sure what a comparison function would be for this function.

 

Let me try...so from what I recall, my teacher said that when we are finding a function to compare, we have to look the highest power from each the numerator and denominator of the function. If that is the case, wouldn't you compare it to ln(n)?

 

So you want me to list out how I tested for convergence?

 

oh! Okay...
∑1/(ln2)^n
r = ιrι = ι1/ln 2 ι ≥1 so, divergent by geometric series.

P.S. how do you put the math thingies in this thing....I'm very new, and I'm confused. :/

 

Yes, but the integral test is barely used...

 

That was literally the only one that I found...