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Math Help - Checking this series for convergence

  1. #1
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    Checking this series for convergence

    Hi all,

    I'm new to this, and am looking at the following series:



    I decided to apply the ratio test and came up with the following:



    This gives me a rho value of 1, telling me absolutely nothing. My question is if my approach was valid, or if I should have cancelled some terms that I didn't cancel. Did I do this right?

    Also, how would you approach this series to test convergence?
    Last edited by mr fantastic; April 21st 2011 at 02:22 PM. Reason: 'Fixed' latex
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  2. #2
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    Thanks Mr. Fantastic...what happened with the latex? I was checking to see where I made a mistake.... What is the correct type of latex for here? I should have had that formatted for LaTeX 2.09 and greater.

    Edit: Nevermind....I see the other posts on the board regarding this issue now.
    Last edited by Malaclypse; April 21st 2011 at 02:46 PM.
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  3. #3
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    Quote Originally Posted by Malaclypse View Post
    Hi all,

    I'm new to this, and am looking at the following series:



    I decided to apply the ratio test and came up with the following:



    This gives me a rho value of 1, telling me absolutely nothing. My question is if my approach was valid, or if I should have cancelled some terms that I didn't cancel. Did I do this right?

    Also, how would you approach this series to test convergence?
    Your cancelling is wrong. You should have got .
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  4. #4
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    Thank you. That's where I figured I was going horribly wrong, but where I'm struggling is understanding just how those terms cancel. Is it basically because the (3n-2) and the (2n-1) exist in previous terms?

    I'm having a hard time seeing it as an obvious fact....but I suppose that's what practice is for.
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  5. #5
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    Quote Originally Posted by Malaclypse View Post
    Thanks Mr. Fantastic...what happened with the latex? I was checking to see where I made a mistake.... What is the correct type of latex for here? I should have had that formatted for LaTeX 2.09 and greater.

    Edit: Nevermind....I see the other posts on the board regarding this issue now.
    Read the relevant threads: http://www.mathhelpforum.com/math-help/f26/
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  6. #6
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    Quote Originally Posted by Malaclypse View Post
    Thank you. That's where I figured I was going horribly wrong, but where I'm struggling is understanding just how those terms cancel. Is it basically because the (3n-2) and the (2n-1) exist in previous terms?

    [snip]
    Yes.

    Write the last two terms in the numerator and denominator of the second product term to see it.
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  7. #7
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    I'll be sure to remember to do that with future recursive looking formulas. Thanks!
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