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Using root test and ratio test for divergence

  1. Mar 18, 2007 #1
    1. The problem statement, all variables and given/known data

    Does this series converge or diverge?

    Series from n=1 to infinity n(-3)^(n+1) / 4^(n-1)

    2. Relevant equations

    3. The attempt at a solution

    Okay, I've tried it both ways.

    Ratio test:

    lim n --> inf. ((n+1)*(-3)^(n+1)/4^n) / (n * (-3)^n / 4^(n-1))

    Now, that doesn't appear to simplify in anyway that would make using l'hospital's rule possible to find the limit.

    Root test:

    lim n --> inf. of -3*n^(1/n) / 4^((n-1)/n)

    That bottom part throws me off.
  2. jcsd
  3. Mar 19, 2007 #2
    Why does it through you off? What is the limit of (n-1)/n as n goes to infinity?
  4. Mar 19, 2007 #3


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    Staff Emeritus
    Science Advisor

    Seriously? You are aware, are you not, that (-3)^(n+1)/(-3)^n= -3? The (4^n part is just as easy! You should not need L'Hospital's rule.

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