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Sum of Series

  1. Feb 20, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the sum of the series.

    Summation (n/2^n)
    from n = 1 to inf

    2. Relevant equations

    Summation (x^n) = 1/1-x

    3. The attempt at a solution


    Not sure what this equals after this... I was thinking (1/1-0.5) but that is a guess.
    There are other ones like this, i have no idea how to do them, so any help on how to start and/or finish them will be appreciated.
  2. jcsd
  3. Feb 20, 2008 #2


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    Have you covered uniform convergence of series?
  4. Feb 20, 2008 #3
    I...don't know. Ik that the terms themselves converge to zero, but I dont know how to calc the sum...
  5. Feb 20, 2008 #4


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    Differentiate Summation(x^n)=1/(1-x). Put x=1/2.
  6. Feb 21, 2008 #5


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    This is what I had in mind, but don't we need uniform convergence to justify differentiating under the sum?

    I remember doing this problem w/o this trick a year ago. It involved rearanging the series if my memory serves me right.
  7. Feb 21, 2008 #6
    What do I do about the extra n in front then?
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