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Homework Help: 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

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    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

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    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

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    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

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    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

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    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 =)
     
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