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Homework Help: Radius and interval

  1. Jul 27, 2008 #1
    1. The problem statement, all variables and given/known data

    Finding the Radius of interval convergence of [tex]\sum[/tex] n=1(theres a infinity on the sigma), "x^n/2^n"

    I really dont have a clue on which way I should go.
    Just a hint would be great:)

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 27, 2008 #2

    Dick

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    Homework Helper

    Hint: ratio test.
     
  4. Jul 27, 2008 #3

    HallsofIvy

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    You almost always use the ratio test to find the radius of convergence of a power series. For this particular problem you may find that the root test is simpler. But for most power series the ratio test is simplest.

    Ratio test: The series [itex]\sum a_n[/itex] converges absolutely if
    [tex]\lim_{n\rightarrow \infty}\frac{a_{n+1}}{a_n}< 1[/itex]
    It diverges if that limit is larger than one and may converge absolutely, converge conditionally, or diverge if the limit is equal to 1.

    Root test: The series [itex]\sum a_n[/itex] converges absolutely if
    [tex]\lim_{n\rightarrow \infty}\left( ^n\sqrt{a_n}\right)< 1[/itex]
    It diverges if that limit is larger than one and may converge absolutely, converge conditionally, or diverge if the limit is equal to 1.
     
    Last edited by a moderator: Jul 27, 2008
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