Recent content by grossgermany

and therefore it diverges?

initial n=2

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.

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?

Most unfortunately both ratio test and limit comparison test give you 1 which is inconclusive.

No sir, 1/[n(log(n))] diverges, comparison test would not help in this case.

Homework Statement Does 1/[n(log(n))^2] converge or diverge Homework Equations We know that Does 1/[n(log(n))] diverges by integral testThe Attempt at a Solution

Yes, however the integral doesn't work in this particular case Note that the question says nlog(n+1), not nlogn

Homework Statement Why does the series 1/[nlog(n+1)] diverge 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. The Attempt at a Solution

Homework Statement Prove that the series: 1/[n log(n)]^1.1 converges Homework Equations 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.

Yes, comparison test would be great.

Homework Statement How to show that sqrt(4n)/sqrt(4n-3)sqrt(4n^2-3n) diverges? Homework Equations 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 for the...

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.

Yes, this is for real analysis class

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