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Power Series

  1. Mar 2, 2010 #1
    1. The problem statement, all variables and given/known data

    Consider the power series

    Σanxn = 1+2x+3x2+x3+2x4+3x5+x6+…

    in which the coefficients an=1,2,3,1,2,3,1,... are periodic of period p=3. Find the radius of convergence.

    2. Relevant equations

    3. The attempt at a solution
    My attempt at a solution was to first state that the series was geometric as r=x
    In order for this series to converge, the absolute value of r must be less than 1.
    Therefore |x|<1.
    Based on this, the interval of convergence is (-1,1) and the radius is r=1.

    Based on my solution, I did not take into account an.... If there is another solution I would need to take an into account to solve the radius of convergence please let me know.
  2. jcsd
  3. Mar 2, 2010 #2


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    Homework Helper

    What if x is negative? Then you'd have an alternating series. You have to consider where this series converges.
  4. Mar 2, 2010 #3


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    Science Advisor
    Homework Helper

    But the series isn't a geometric series. So you don't know |x|<1 yet. You can split it up into some series that are geometric, though.
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