# Convergence or Divergence?

1. Oct 27, 2008

### fiziksfun

$$\sum$$$$\frac{1*3*5 ... (2k-1)}{1*4*7 ... (3k-2)}$$

from k=1 to infinity

Does this series converge or diverge??

I have no idea where to begin, I don't understand it's format. Aren't series usually A+B+C ... but this is just multiplication ???!

? So ?? HELP!!

Last edited: Oct 27, 2008
2. Oct 27, 2008

### jhicks

It is a summation...maybe? You have indicated SOMETHING by using $$\Sigma$$. However, your use of it is vague enough that I cannot tell whether you mean to sum say 1 + 1*3/1*4 + 3*5/4*7 + etc... or the entire thing is just one term.

3. Oct 27, 2008

### HallsofIvy

Staff Emeritus
Are you saying you don't know what "$\sum$" means? Obviously this IS a sum. Each of the "A", "B", and "C" being summed involves a product.

Do you remember a very simple theorem about when a sum does not converge?

4. Oct 27, 2008

### fiziksfun

Does it diverge because the lim as k approaches infinity is 2/3 ?

5. Oct 27, 2008

### JinM

I recall having had something similar in Calculus II. Have you tried Ratio test? It's probably more approachable that way.

6. Oct 27, 2008

### HallsofIvy

Staff Emeritus
No. The limit of the terms is NOT 2/3. Use the ratio test as JinM suggested.

7. Oct 27, 2008

### fiziksfun

Is the limit 1?

8. Oct 27, 2008

### jhicks

Don't make wild guesses. You aren't learning anything that way. All the question is asking is for convergence/divergence of the sum. Use the ratio test.