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Check my solution

  1. May 1, 2014 #1
    1. The problem statement, all variables and given/known data

    The coefficients of the power series the sum from n=0 to infinity of an (x-2)^n satisfy ao=5 and an= [(2n+1)/(3n-1)] an-1 for all n is greater than or equal to 1. The radius of convergence of the series is

    A) 0 B) 2/3 C) 3/2 D) 2 E) infinite

    2. Relevant equations



    3. The attempt at a solution

    Convergence test: lim n→∞|an (x-2)^n / an+1 (x-2)^n+1|
    2/3*|1/(x-2)|<1
    x belongs to (4/3, 8/3)
    Therefore, the radius is 2/3
     
  2. jcsd
  3. May 1, 2014 #2

    LCKurtz

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    For the ratio test you use the n+1 term over the n term ( or n over n-1). You have it upside down.

    3. The attempt at a solution
     
  4. May 1, 2014 #3

    Ray Vickson

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    Use parentheses! What you wrote means
    [tex] a_n= \frac{2n+1}{3n-1} a_n - 1[/tex]
    but I suspect you mean
    [tex]a_n= \frac{2n+1}{3n-1} a_{n - 1}[/tex]
    In ASCII you should write a_n = [(2n+1)/(3n-1)] a_(n-1) or a(n)= [(2n+1)/(3n-1)] a(n-1)
     
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