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Homework Help: Power Series(Radius and interval of convergence)

  1. Dec 10, 2009 #1
    hey there.. i hope u guys can help me..
    the question is...
    Determine the interval and radius of convergence of the power series below..
    [tex]\sum\limits_{k=0}^\infty[/tex]k!(x-3)^k

    i've already find the radius, r = 0
    then..
    c - r < x < c + r
    3 - 0 < x < 3 + 0
    hence, x = 3

    when x = 3..
    [tex]\sum\limits_{k=0}^\infty[/tex]k!(3-3)^k = 0

    so.. the interval of convergence is 0
    am i do it right?
     
  2. jcsd
  3. Dec 10, 2009 #2

    HallsofIvy

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    Science Advisor

    No, the interval of convergence is an interval- a set of points, not a number. Since the radius of convergence is 0, the "interval" of convergence is the single point {3}
     
  4. Dec 10, 2009 #3
    Got it!!! Thanks!! =)
     
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