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Convergence or Divergence?

  1. Oct 27, 2008 #1
    [tex]\sum[/tex][tex]\frac{1*3*5 ... (2k-1)}{1*4*7 ... (3k-2)}[/tex]

    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. jcsd
  3. Oct 27, 2008 #2
    It is a summation...maybe? You have indicated SOMETHING by using [tex]\Sigma[/tex]. 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.
     
  4. Oct 27, 2008 #3

    HallsofIvy

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    Are you saying you don't know what "[itex]\sum[/itex]" 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?
     
  5. Oct 27, 2008 #4
    Does it diverge because the lim as k approaches infinity is 2/3 ?
     
  6. Oct 27, 2008 #5
    I recall having had something similar in Calculus II. Have you tried Ratio test? It's probably more approachable that way.
     
  7. Oct 27, 2008 #6

    HallsofIvy

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    No. The limit of the terms is NOT 2/3. Use the ratio test as JinM suggested.
     
  8. Oct 27, 2008 #7
    Is the limit 1?
     
  9. Oct 27, 2008 #8
    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.
     
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