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Don't understand how they simplified this (ratio test)

  1. Nov 13, 2007 #1
    Don't understand how they simplified this....(ratio test)

    I'm studying for my exam and I was looking at this example:

    [​IMG]



    I'm not really sure how they get from here :

    [​IMG]

    to here:

    [​IMG]


    If someone could explain how they simplified this to me that would be fantastic...i'm really trying to understand series but sometimes the algebra stuff holds me up :-(.
     
  2. jcsd
  3. Nov 13, 2007 #2
    You are basically just dividing like terms, so you subtract exponents

    (-3)^n+2 / (-3)^n+1 = (-3)^ ((n+2)-(n+1)) = -3

    2^3n / 2^(3n+3) = 2^((3n) -(3n+3)) = 2^-3

    hope that helps
     
  4. Nov 13, 2007 #3
    yes that helps...thank you :-)
     
  5. Nov 13, 2007 #4
    actually that helped a lot... thank you thank you!
     
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