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Interval of convergence?

  1. Jan 11, 2014 #1
    1. The problem statement, all variables and given/known data

    serie ((-1)^(n-1)(x-2)^(n-1))/(5^n)

    2. Relevant equations
    how to find the interval of convergence for this?


    3. The attempt at a solution
     
  2. jcsd
  3. Jan 11, 2014 #2

    tiny-tim

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    Science Advisor
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    hi alnix! :smile:

    (try using the X2 button just above the Reply box :wink:)

    first, simplify it to something you can recognise!
     
  4. Jan 11, 2014 #3
    Before we can go anywhere, is this what you mean?
    [tex]\frac{(-1)^{n-1}(x-2)^{n-1}}{5^n}[/tex]
     
  5. Jan 11, 2014 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    The simplest way to determine the radius of convergence is to use the "ratio test".
    [tex]a_n= \frac{(-1)^{n-1}(x- 2)^{n-1}}{5^n}[/tex]
    [tex]a_{n+1}= \frac{(-1)^n(x- 2)^n}{5^{n+1}}[/tex]

    What is [itex]\left|\frac{a_{n+1}}{a_n}\right|[/itex]? What is the limit of that as n goes to infinity? For what x is that limit less than 1?
     
  6. Jan 13, 2014 #5

    Mark44

    Staff: Mentor

    To all who have responded in this thread - if someone posts a problem with no effort shown, please use the Report button to let the mentors know.

    Alnix, I am closing this thread. Please start a new thread and be sure to show what you have attempted.
     
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