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Calculate the sum of the series

  1. Jul 23, 2011 #1
    so i am having trouble calculating the sum of the series of
    (1+2^x)/(3^x) from 1 to infinity
    i rearranged it and made a geometric series where r =2/3 and got that it converges toward 2. however the answer is 2.5? This problem shouldnt need any tests as its it a section of the book that hasant taught any of the tests, except for geometric so what am I doing wrong. I have been stuck on this for hours now? :(
     
  2. jcsd
  3. Jul 23, 2011 #2

    SammyS

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    Let's see details for how you went about getting your result.
     
  4. Jul 23, 2011 #3
    You forgot about the 1 in the numerator:

    [tex]\sum \frac{1 + 2^x}{3^x} = \sum \left(\frac{1}{3^x} + \frac{2^x}{3^x} \right) = \sum \frac{1}{3^x} + \sum \left(\frac{2}{3}\right)^x = ?[/tex]
     
  5. Jul 24, 2011 #4
    Borhok has the right method again.
    Shemer77, would you let us know if you've gotten the right answer from Bohrok's information or still have further questions? Thanks.
     
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