1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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

  1. Jul 9, 2013 #1
    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


    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
    After this part how i will decide parantesis will be closed or open?

    Attached Files:

  5. Jul 9, 2013 #4


    User Avatar
    2017 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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted