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Ratio Test Help

  1. Apr 5, 2015 #1
    1. The problem statement, all variables and given/known data
    I'm reviewing for a test and working on the practice problems for the ratio test that Pauls Online Notes gives. So here is given problem:
    eq0001MP.gif

    Here is his solution for the problem:
    eq0002MP.gif


    2. The attempt at a solution
    I worked this out before I looked at the solution and I got it wrong. I had it right up until the 4th step. Can someone explain this step to me? I don't understand why the (n-1)! is broken up into (n-1)(n-2)! Isn't this supposed to be the decomposition of (n-2)!? I'm sorry if this is a stupid question, I'm just trying to learn from my mistakes so that I won't do this again.

    Thanks for stopping by!
     
  2. jcsd
  3. Apr 5, 2015 #2

    WWGD

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    Not sure I understand your question; (n-1)! =(n-1)(n-2)...2.1= (n-1)[(n-2)(n-3)...2.1]= (n-1)(n-2)! is a decomposition of (n-1)!
     
  4. Apr 5, 2015 #3
    Then what is the decomposition on (n-2)! ?
     
  5. Apr 5, 2015 #4

    WWGD

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    In this format, it is (n-2)(n-3)! . In general, (n-k)!= (n-k)(n-k-1)! if n>k, to avoid a -1!.
     
  6. Apr 5, 2015 #5
    Thank you so much!! This helps me out tremendously!
     
  7. Apr 5, 2015 #6

    WWGD

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    Glad it helped, mmont012.
     
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