Convergence or Divergence of a Series with Multiplication Terms?

[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!

 

[jhicks]

Aren't series usually A+B+C ... but this is just multiplication ?!

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.

 

[HallsofIvy]

\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!

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?

 

[fiziksfun]

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

 

[JinM]

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

 

[HallsofIvy]

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

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

 

[fiziksfun]

Is the limit 1?

 

[jhicks]

Is the limit 1?

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.