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

Complex Series, Region of Convergence

  1. Nov 30, 2011 #1
    Good evening, I'm an electrical engineering student questioning my answer to this series Region of Convergence problem.

    Ʃ(0,inf) (n(n-1)(z+5i)^n)/n

    Using the ratio test lim n-> |an+1/an|

    I was able to get it down to lim n->|n(z+5i)/(n-1)| which gave |inf/inf| = 1, which means the test fails. What do I do to properly solve this? :(
     
  2. jcsd
  3. Nov 30, 2011 #2

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    you can't just write it as inf/inf and cancel them!
    [tex] \lim_{n\to \infty} |\frac{n(z+5i)}{n-1}| = |z+5i| \lim_{n\to \infty} \frac {n}{n-1} [/tex]
     
  4. Nov 30, 2011 #3
    ROC
    = |z+5i| < inf?

    :D
     
  5. Nov 30, 2011 #4

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Once you know the limit is |z+5i|, what does this have to be smaller than for the series to converge?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Complex Series, Region of Convergence
  1. Series Converges. (Replies: 5)

Loading...