Convergence or Divergence of a Series with Multiplication Terms?

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Homework Help Overview

The discussion revolves around the convergence or divergence of a series defined by a summation involving products in both the numerator and denominator. The series is presented in a format that combines multiplication terms, which has led to confusion among participants regarding its structure and interpretation.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants express uncertainty about the series format, questioning whether it constitutes a valid summation. There are discussions about the interpretation of the summation notation and the nature of the terms being summed. Some participants suggest using the ratio test as a potential method for analyzing convergence.

Discussion Status

The discussion is active, with participants exploring different interpretations of the series and questioning assumptions about the limit of the terms. Guidance has been offered regarding the use of the ratio test, although there is no explicit consensus on the convergence or divergence of the series at this stage.

Contextual Notes

Participants are grappling with the format of the series and the implications of using products within the summation. There is a noted lack of clarity about the limit of the terms as k approaches infinity, which is central to determining convergence or divergence.

fiziksfun
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\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!
 
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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.
 
fiziksfun said:
\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?
 
Does it diverge because the lim as k approaches infinity is 2/3 ?
 
I recall having had something similar in Calculus II. Have you tried Ratio test? It's probably more approachable that way.
 
fiziksfun said:
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.
 
Is the limit 1?
 
fiziksfun said:
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.
 

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