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Power Series Convergence

  1. Sep 22, 2010 #1
    1. The problem statement, all variables and given/known data
    If [tex]\sum_{n=0}^{\infty} c_{n}4^n[/tex] is convergent, does it follow that the following series are convergent?

    a) [tex]\sum_{n=0}^{\infty} c_{n}(-2)^n[/tex] b) [tex]\sum_{n=0}^{\infty} c_{n}(-4)^n[/tex]


    2. Relevant equations
    The Power Series: [tex]\sum_{n=0}^{\infty} c_{n}(x - a)^n[/tex]


    3. The attempt at a solution
    I was able to work all the problems that asked me to solve for a radius of convergence, but this question seems much different, and I can't think about how to prove or disprove either a or b. Any tips would be much appreciated.
     
  2. jcsd
  3. Sep 23, 2010 #2

    hunt_mat

    User Avatar
    Homework Helper

    If you know that:
    [tex]
    \sum_{n=0}^{\infty} c_{n}4^n
    [/tex]
    Then apply the ratio test on this to get a relationship between c_{n} and c_{n+1}, then you can use this to check the other series . Look up the alternating series test also.
     
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