1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Power Series(Radius and interval of convergence)

  1. Dec 9, 2009 #1
    hey there..
    i've try this question(attachment) already...
    i got radius of convergence, R = 1/8

    at x = 1/8,
    converges...

    at x = -1/8
    i don't how to do this one..
    please help me..
     

    Attached Files:

  2. jcsd
  3. Dec 9, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    How did you conclude that has radius of convergence 1/8?? Your bmp has an n! in the denominator. What does the ratio test tell you?
     
  4. Dec 9, 2009 #3
    to find the radius, r..
    i use an / an+1
     
  5. Dec 9, 2009 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Go ahead. Use it. What the limit of the ratio?
     
  6. Dec 9, 2009 #5
    then.. i got radius = 1/8
     
  7. Dec 9, 2009 #6

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    What's the ratio an/an+1? I don't think you are getting that limit right.
     
  8. Dec 9, 2009 #7
    i've revised back my calculation..
    should i get infinity for my radius..
     
  9. Dec 9, 2009 #8

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Yes.
     
  10. Dec 9, 2009 #9
    ok.. so.. i need to check the interval of convergence..

    when x = infinity,
    the series will converges..

    when c = -infinity,
    the series will converges too..

    hence, my interval of convergence is (-infinity,infinity)

    am i right?
     
  11. Dec 9, 2009 #10

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    It converges for ALL x, that's what you mean, right? There's no such number as +infinity or -infinity. They are only limits you approach. You don't have to check them.
     
  12. Dec 9, 2009 #11
    alright! i understand now..
    Thanks Dick =)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook