# Convergent or Divegent Series?

1. Dec 9, 2008

### iatnogpitw

1. The problem statement, all variables and given/known data
$$\sum{(ln(k))/(\sqrt{k+2})}$$, with k starting at 1 and going to $$\infty$$

2. Relevant equations
Does this series converge or diverge? Be sure to explain what tests were used and why they are applicable.

3. The attempt at a solution
Okay, my TA got that this diverges, but I got that it converges by simply taking the limit as k goes to $$\infty$$ and applying L'Hopital's rule. I also plugged the function into my calculator and it seems to converge at y=0, which is corroborates what I got with L'Hopitals rule. What did you guys get? Any help is greatly appreciated.

2. Dec 9, 2008

### Office_Shredder

Staff Emeritus
It looks like you proved the individual terms go to 0, which isn't what you're trying to do. The definition of a series is you take the limit of the partial sums. And where does y come into the series?

Try comparing the series to $$\frac{1}{\sqrt{k+2}}$$ whose convergence/divergence is easier to find

3. Dec 9, 2008

### iatnogpitw

Right, I forgot about the partial sums. Thanks, that helped a lot. But isn't $$1/(\sqrt{k+2})$$ smaller than $$(ln(k))/(\sqrt{k+2})$$?

Last edited: Dec 9, 2008
4. Dec 9, 2008

### Staff: Mentor

Yeah, it is. You've been handed a clue for free. If you can say something about what $$\sum 1/(\sqrt{k+2})$$ does, then maybe you will know something about the series you're really interested in.