# Series Convergence and Divergence test!

## Homework Statement

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

## Homework 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).

## The Attempt at a Solution

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mfb
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?

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

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

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

mfb
Mentor
Then which part of the answer was unclear?

Then which part of the answer was unclear?
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.

Ray Vickson
Homework Helper
Dearly Missed
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.
We cannot give you more hints without essentially doing the question for you.

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

mfb
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?

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

mfb
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)?

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. :/

mfb
Mentor
oh! Okay...
∑1/(ln2)^n
r = ιrι = ι1/ln 2 ι ≥1 so, divergent by geometric series.
That is certainly not the only one you had before.

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

LCKurtz
Homework Helper
Gold Member
Another test you might consider is the integral test.

Another test you might consider is the integral test.
Yes, but the integral test is barely used...

That is certainly not the only one you had before.

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

LCKurtz