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Homework Help: Once i find the radius of convergence, how do i find the interval of convergence?

  1. Mar 9, 2006 #1
    Hello everyone, i'm confused (as usual). I think i found the radius of convergence but then waht do i do to find the interval on which it converges?

    The directions says:
    Find all the values of x such that the given series would converge.
    http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/70/aaf16ffcdb10d6976585856b5dafca1.png [Broken]
    The series is convergent
    from x = , left end included (enter Y or N):
    to x = , right end included (enter Y or N):

    Here is my work:
    http://img90.imageshack.us/img90/6637/lastscan5ox.jpg [Broken]

    Any help would be great! thankss!
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Mar 9, 2006 #2
    OKay i had to of messed up finding the radius of convergence. I looked at a tutoiral and it should be right...
    I got
    (-7,7); for the interval, which was wrong though. Can you see where i screwed it up? it should be open brackets i got that part right

    Okay i did it again, and i tried (-14,14), now i have 75% of the question rgiht, so either -14 is wrong or 14 is wrong but i don't see how u can get any other number then that.
    if u have
    |(x-7)/7| < 1

    |(x-7)/7| > 1
    Last edited: Mar 9, 2006
  4. Mar 9, 2006 #3


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    Science Advisor

    Why did [itex]\left|\frac{x-7}{7}\right|< 1[/itex] become x-7< 7??
    Shouldn't it be |x-7|< 7? And doesn't that mean that -7< x- 7< 7?
    So that 0< x- 7< 14?
  5. Mar 9, 2006 #4
    Thanks Ivey ur the man! i forgot all about that rule!
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