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Homework Help: Finding Intervals of Convergence

  1. Apr 11, 2010 #1
    Find the interval of convergence for the given power series.
    [PLAIN]http://img52.imageshack.us/img52/3632/c1786dba870d63ff1a827d9.png [Broken]
    The series is convergent
    from x= ___ to
    x = ____

    Attempt


    [PLAIN]http://img412.imageshack.us/img412/7411/image00.jpg [Broken]


    Attempted solutions:

    I have to input the answer into something called WeBWorK and i've tried a bunch of different pairs of number, the only ones i remember try were

    0, 8
    0, 4
    0, -8

    among many others.

    Can anyone tell me what I'm doing wrong?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 11, 2010 #2

    LCKurtz

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    You have a sign mistake. You should get

    [tex]\left| \frac{x-4} 4\right| < 1[/tex]

    so

    [tex]-1 < \frac{x-4} 4 < 1[/tex]
     
  4. Apr 11, 2010 #3
    Well after simplifying that inequality, I get the intervals to be (x=0, x=8), and like I said before, it still isn't correct.

    Did I make a mistake somewhere else?
     
  5. Apr 11, 2010 #4

    LCKurtz

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    No. It converges on (0,8). The only remaining question is whether it converges at the two end points, 0 and 8, which need to be checked separately. You might need to give an answer in one of these forms:

    (0,8), [0,8), (0,8], [0,8]

    where the square bracket indicates convergence at that end. Check x = 0 and x = 8.
     
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