Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    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.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook