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Power series

  1. Jul 9, 2013 #1
    Hello,
    My question is about power series.
    In most of questions i can find points with ratio test.
    But when i check points i cant understand style of parenthesis.
    Is there easy way?
    For example:[itex]\sum(n^(3)*(x-5)^n)[/itex]
    I found check points 4<x<6
    How can i decide to the parenthesis will be closed or open?

    Thank you
     
  2. jcsd
  3. Jul 9, 2013 #2
    I don't understand anything from this. What paranthesis? What style? And how do you find points with the ratio test? It is supposed to give you a boundary condition on x, you aren't supposed to obtain a point.
     
  4. Jul 9, 2013 #3
    I uploaded question this is not a homework i just trying to understand how we decide to the
    boundaries of covergence. Also i dont know how i can write mathematicaly here.

    Lim n->inf |((n+1)^(3)*(x-5))^(n+1)/(n^(3)*(x-5)^n)

    Lim n->inf |(x-5)*(((n+1)/n)^3)| after x-5 this part equal to the 1

    -1<|x-5|<1
    4<x<6

    Then i tried to check points;
    I put this points to the question
    Ʃ[0,inf]n^(3)*(x-5)^n = Ʃ[0,inf]n^(3)*(4-5)^n
    Ʃ[0,inf]n^(3)*(-1)^n
    After this part how i will decide parantesis will be closed or open?
     

    Attached Files:

  5. Jul 9, 2013 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    If you know LaTeX: [tex]a^2+b^2[/tex] gives [tex]a^2+b^2[/tex]

    You mean the interval borders? You have to check them separately. Just set x to the corresponding value, and see if the series converges.
     
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