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Power series, driving me mad

  1. May 4, 2005 #1
    summation from n=1 to infinity (x-2)^n/(n*3^n).

    My teacher got -1 <= x<= 5 as the interval of convergence because he found that x-2/3<1

    Using the ratio test i get (x-2)n/(n+1)3, consistantly. This is driving me wild. :rofl:
  2. jcsd
  3. May 4, 2005 #2


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    Did you remember to take the limit?
  4. May 4, 2005 #3
    [tex]\sum_{n=1}^{\infty} \frac{(x-2)^n}{n3^n}[/tex]

    So using the ratio test we get,


    This reduces to


    Which further reduces to...


    So, evaluating the limit we get:

    [tex]\frac{{\mid}x-2{\mid}}{3} < 1[/tex]

    I think Hurkyl's advice was easier than my work.
    Last edited: May 4, 2005
  5. May 4, 2005 #4
    ah yes, thats it! i forgot the limit. thank you
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