# Recent content by grossgermany

1. ### Does 1/n(log(n))^2 converge or diverge

and therefore it diverges?

initial n=2
3. ### Does 1/n(log(n))^2 converge or diverge

Yes, the integral test, however please tell me how to evaluate this integral? I suspect the result would be some expression that goes to infinity.
4. ### Does 1/n(log(n))^2 converge or diverge

Unfortunately I have never tried the Ei(u) thing. Nor have I heard of integral function. In other words 1/[n(log(n))^2] diverges?
5. ### Does 1/n(log(n))^2 converge or diverge

Most unfortunately both ratio test and limit comparison test give you 1 which is inconclusive.
6. ### Does 1/n(log(n))^2 converge or diverge

No sir, 1/[n(log(n))] diverges, comparison test would not help in this case.
7. ### Does 1/n(log(n))^2 converge or diverge

1. Homework Statement Does 1/[n(log(n))^2] converge or diverge 2. Homework Equations We know that Does 1/[n(log(n))] diverges by integral test 3. The Attempt at a Solution
8. ### Why does 1/[nlog(n+1)] diverge

Yes, however the integral doesn't work in this particular case Note that the question says nlog(n+1), not nlogn
9. ### Why does 1/[nlog(n+1)] diverge

1. Homework Statement Why does the series 1/[nlog(n+1)] diverge 2. Homework Equations We know that 1/[nlog(n)] diverges by the integral test. However the question as written does not lend itself to be any integral precisely. 3. The Attempt at a Solution
10. ### Why does 1/[n log(n)]^1.1 converge

1. Homework Statement Prove that the series: 1/[n log(n)]^1.1 converges 2. Homework Equations 3. The Attempt at a Solution We know that nlogn is equal to d[log(log(n))] and use the integral test to show that it diverges. However, I have no idea how to deal with the 1.1th power.
11. ### Sqrt(4n)/sqrt(4n-3)sqrt(4n^2-3n) diverges?

Yes, comparison test would be great.
12. ### Sqrt(4n)/sqrt(4n-3)sqrt(4n^2-3n) diverges?

1. Homework Statement How to show that sqrt(4n)/sqrt(4n-3)sqrt(4n^2-3n) diverges? 2. Homework Equations 3. The Attempt at a Solution The above expression is asymptotically equivalent to 1/2n which diverges as the harmonic series diverges. However, a rigorous proof is required...
13. ### Does limit ln(n)/n^c -> 0 for any c>0?

Yes, we can use Bolzano Weierstrasse Theorem. Please feel free to proceed. My level is on baby Rudin, the this is the first course in real analysis.
14. ### Does limit ln(n)/n^c -> 0 for any c>0?

Yes, this is for real analysis class
15. ### Does limit ln(n)/n^c -> 0 for any c>0?

1. Homework Statement Does limit ln(n)/n^c -> 0 for any c>0? 2. Homework Equations 3. The Attempt at a Solution I wonder if there is an 1.Epsilon Delta Proof 2.Proof using BigO SmallO notation. Thanks