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Find the interval of convergence

  1. Dec 10, 2015 #1
    1. The problem statement, all variables and given/known data
    Find the interval of convergence of the power series ∑(x-2)n / 3n

    2. Relevant equations
    ρn = |an+1| / |an|

    3. The attempt at a solution
    I got that ρn = | (x-2) / 3 |. I set my ρn ≤ 1, since this is when the series would be convergent. Manipulating that expression, I got that the interval of convergence is -5 ≤ x ≤ 5. The answer in the back of the book is -1 ≤ x ≤ 5. I am confused where the -1 comes from.
     
  2. jcsd
  3. Dec 10, 2015 #2
    I'm sorry, I realized after this post that I was getting interval of convergence mixed up with radius of convergence.
     
  4. Dec 10, 2015 #3

    Ray Vickson

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    Science Advisor
    Homework Helper

    Be careful: the endpoints are generally not included, because they would correspond to a series of the form ##\sum 1^n## or ##\sum (-1)^n##. Are you sure the book did not say ##-1 < x < 5##?
     
  5. Dec 13, 2015 #4
    You're right, it does say -1 < x < 5. Thank you for that reminder!
     
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