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Homework Help: Power series

  1. May 22, 2005 #1
    How do you know what value a power series is centered at?

    for example this power series is centered at 0:

    [tex]\sum_{n=0}^\infty\frac{x^n}{n!}[/tex]


    what makes it centered at zero?



    this one is centered at -1:

    [tex]\sum_{n=0}^\infty{(-1)}^n{(x+1)}^n[/tex]

    the only thing i can discern is that when i perfrom the ratio test, for the secont series, i get this expression:

    [tex]\lim_{n\rightarrow\infty}\vert{(-1)(x+1)}\\\vert[/tex] which is supposed to be less than 1.


    what's the latex for the lessthan symbol?
     
    Last edited: May 22, 2005
  2. jcsd
  3. May 22, 2005 #2
    I see it now no need to respond. thx
     
  4. May 22, 2005 #3

    Hurkyl

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    <


    \leq for "less than or equal to".
     
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