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Interval of convergence

  1. Nov 24, 2006 #1

    fsm

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    I just wanted to see if someone could verify my answers:

    [tex]
    \\sum_{n=0}^\\infty \\frac{(x+7)^n}{sqrt(n)}
    [/tex]
    I get:
    -8<x<-6

    [tex]
    \\sum_{n=1}^\\infty \\frac{(-1)^n*x^2n}{n!}
    [/tex]
    This one I'm not sure of. When I take the limit I get 0. When I solve the inequality I get x. I can't find an example of this.
     
  2. jcsd
  3. Nov 24, 2006 #2

    fsm

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    This might be better:
    [​IMG]
     
  4. Nov 24, 2006 #3
    1. correct



    2. [tex]\sum_{n=1}^{\infty} \frac{(-1)^{n}x^{2n}}{n!} [/tex]


    [tex] |\frac{(-1)^{n+1}x^{2n+1}}{n!(n+1)}\frac{n!}{(-1)^{n}x^{2n}} = \frac{x}{n+1} \rightarrow 0 [/tex]. Thus the interval of convergence is [tex] (-\infty, \infty) [/tex]
     
    Last edited: Nov 24, 2006
  5. Nov 24, 2006 #4

    fsm

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    I don't understand your answer for #2. I got the same thing but how is this the interval of convergence?
     
  6. Nov 24, 2006 #5
    What don't you understand about it?
     
  7. Nov 24, 2006 #6

    fsm

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    All the stuff to the right of the equal sign now just appeared. Thanks for the help.
     
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