# Converge or Diverge?

1. Nov 2, 2012

### catsfanj

1. The problem statement, all variables and given/known data
Ok, so I was given this problem:

Ʃ (kth root of k)/k^3 = k^(1/k) / k^3
k=1

2. Relevant equations
None

3. The attempt at a solution
I know that I have to use the comparison test, but am unsure how to apply it. Can somebody help me?

2. Nov 2, 2012

### clamtrox

You can write that into Ʃk1/k-3. Can you find a nice real number r that has the property that r>1/k-3 for all k and Ʃkr converges?

3. Nov 2, 2012

No I can't.

4. Nov 2, 2012

### micromass

Staff Emeritus
Can you tell us for which real numbers r, the series $\sum_k k^r$ converges?

5. Nov 2, 2012

### catsfanj

I know that the series converges, but do not know what to use for the second series. I need to prove its convergence using one of the tests.

6. Nov 2, 2012

### micromass

Staff Emeritus
What series converges?? What second series??

Can you answer my question about $\sum k^r$?? For which r does it converge?