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I need some peer review of this problem

  1. May 23, 2005 #1
    find the radius and interval of convergence of:

    [tex]\sum_{n=1}^\infty\frac{(-1)^{(n+1)}nx^n}{2^n}[/tex]

    the radius is [tex]x<2[/tex]

    and the interval is [-2,2)

    are these two answers correct?
     
  2. jcsd
  3. May 23, 2005 #2
    Yes

    -- AI
    [edit]
    wait a minute
    just noticed something
    u sure it converges for -2?
    the interval should (-2,2)
    [/edit]
     
    Last edited: May 23, 2005
  4. May 23, 2005 #3
    when i put this in my calculator it adds up at [-2,2).
     
  5. May 23, 2005 #4

    shmoe

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    Step 1) throw away your calculator

    Step 2) check convergence at x= -2 with pencil and paper
     
  6. May 23, 2005 #5
    ah i used the alternating series convergence test incorrectly. by the nth term test for divergence i get that the limit of the series is [tex]\infty[/tex] which is not equal to zero so it diverges.
     
  7. May 23, 2005 #6
    have i come to the correct conclusion shmoe?
     
  8. May 24, 2005 #7

    HallsofIvy

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    At x= 2, the general term is [tex](-1)^{n+1}n[/tex]
    At x= -2, the general term is [tex](-1)^{2n+1}n[/tex]

    The series does not converge at either of those because the term does not go to zero. The interval of convergence is (-2, 2).
     
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