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
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
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.
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...
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