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I Question about the derivative of this sum and where n starts

  1. Jul 5, 2016 #1
    Ok so when differentiating

    1/(1-x)= Σ xn from n=0 to infinity

    the book says it is 1/(1-x)^2 = Σ n*(x)n-1 from n=1 to infinity

    i dont understand why the original sum starts at 0 and then the derived sum starts at 1
  2. jcsd
  3. Jul 5, 2016 #2


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    Both start with the number 1. If you like you may start the second series at 0, too. It doesn't make a difference because ##0 \cdot x^{-1} = 0.## However, in this case one unnecessarily gets into trouble with ##x=0.##
  4. Jul 5, 2016 #3

    Simon Bridge

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    Expand the sum and take the derivative and then rewrite the result in sum notation.
  5. Jul 19, 2016 #4
    both starts with 1 because when you put ##n=0## in first series,the answer will be ##x^0=1##
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