# Series Convergence and Divergence test!

1. Jan 24, 2015

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

2. Jan 24, 2015

### Staff: Mentor

I guess you mean
$$\sum_{n=2}^\infty \frac{\ln(n)}{n}$$
Limit comparison is good. Do you expect it to converge or not? What did you try so far as comparisons?

3. Jan 24, 2015

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

4. Jan 24, 2015

### Staff: Mentor

I'm sure you had convergent or divergent series which had something in common with this expression before. The most useful one is probably the textbook example of a series that gets analzed for convergence.

5. Jan 24, 2015

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

6. Jan 24, 2015

### Staff: Mentor

Then which part of the answer was unclear?

7. Jan 24, 2015

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.

8. Jan 24, 2015

### Ray Vickson

We cannot give you more hints without essentially doing the question for you.

9. Jan 24, 2015

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)?

10. Jan 24, 2015

### Staff: Mentor

It is possible to do that comparison, but it won't tell you anything new.

Can you list series where you checked convergence before?

11. Jan 24, 2015

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

12. Jan 24, 2015

### Staff: Mentor

Now how, but what. At the point where you get those homework problems, you should have tested a few series for convergence before. Can you list them (and the test result)?

13. Jan 24, 2015

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. :/

14. Jan 24, 2015

### Staff: Mentor

That is certainly not the only one you had before.

With LaTeX.

15. Jan 24, 2015

### LCKurtz

Another test you might consider is the integral test.

16. Jan 25, 2015

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

17. Jan 25, 2015

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

18. Jan 25, 2015

### LCKurtz

I have no idea what do you mean by that. It easily works your problem. Have you tried it?

And along the lines of comparison tests, I don't think the "limit comparison test" is what you want anyway. If you think your series diverges try looking for a known divergent series that is smaller.