Does limit ln(n)/n^c -> 0 for any c>0?

[grossgermany]

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

 

[ZioX]

It is obviously true. There are a lot of ways to prove this. What kind of class is this for? Are you expected to be rigorous in your solutions? N-epsilon proofs and asymptotic behaviour are very different arguments in terms of the development required in an analysis setting.

 

[grossgermany]

Yes, this is for real analysis class

 

[ZioX]

What tools do you have available? How was ln(n) derived?

There is a nifty theorem that says that if a sequence converges then any subsequence will converge to the same limit. This will enable you to look at ln(x)/x^c in R rather than in N.

 

[grossgermany]

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.