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Determining whether a sum converges or diverges .

  1. Dec 14, 2011 #1
    Determining whether a sum converges or diverges.....

    1. The problem statement, all variables and given/known data

    Ʃ((3n!)/(4^(n)))

    2. Relevant equations

    I figured I'd do the ratio test with this one.

    3. The attempt at a solution

    So that would be (3(n+1)!)/(4^(n+1)) * (4^(n))/(3n!), I then cross cancel until I'm left with this...

    ((n+1)!)/(4n!) Then you can break up the (n+1)!, to cancel a (n!) in the numerator and denominator, so you're left with the limit as n→∞ of (n+1)/(4), but this doesn't look right to me. Where did I screw up?
     
  2. jcsd
  3. Dec 14, 2011 #2

    SammyS

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    Re: Determining whether a sum converges or diverges.....

    (n+1)/(4) looks right to me !
     
  4. Dec 14, 2011 #3
    Re: Determining whether a sum converges or diverges.....

    But I'm confused regarding the limit of this. Is the limit as n→∞=(1/4)? Well, it becomes (∞/4), so does that diverge. I always get confused when you have infinity on the top, but a constant on the bottom.
     
  5. Dec 14, 2011 #4

    SammyS

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    Re: Determining whether a sum converges or diverges.....

    The ratio goes to ∞ .
     
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