# Homework Help: Does the limit converge or diverge

1. Nov 6, 2011

### kuczmama

1. The problem statement, all variables and given/known data
infinity
Ʃ $\frac{ln(n)}{n\sqrt{n}}$
n=1

2. Relevant equations
I think that I need to use either the limit comparison test or the ratio test.

3. The attempt at a solution

After listing all the terms I found out that the function was positive and decreasing, and that the terms approached 0. However when I used the limit comparison test or the root test I keep on getting an answer of infinity or 0, which is inconclusive. So I don't know how else to approach the problem. Is there something easy that I am overlooking. Thanks.

Last edited by a moderator: Nov 6, 2011
2. Nov 6, 2011

### Staff: Mentor

Show us what you tried for the limit comparison test. I agree that the ratio test would not be conclusive.

3. Nov 6, 2011

### deluks917

I think the best test to use is the ratio test:

If there exists a constant C < 1 such that |an+1/an|<C for all sufficiently large n, then ∑an converges absolutely.

4. Nov 6, 2011

### LCKurtz

Have you thought about the integral test?

5. Nov 6, 2011

### kuczmama

for the limit comparison test I tried a bunch of different comparisons. I said as lim n-> infinity of

lim n→∞. of (ln(n)/(nsqrt(n))/(1/n^5/4).That didnt give me any help. Then I tried comparing it to 1/n^1/4. Then I tried comparing it to a bunch of other stuff but nothing seemed to work. I cant figure out what to do

6. Nov 6, 2011

### kuczmama

Also I never thought about the integral test. I will try that

7. Nov 6, 2011

### LCKurtz

@kuczmama: Don't use the X2 key inside tex brackets. Right click on this to see how to do exponents:

$$n^{\frac 3 2}$$

8. Nov 6, 2011

### kuczmama

I got that the integral converges to 4. I guess that this means the sum also converges. Thanks alot guys!!