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Homework Help: Closed form of power series

  1. Jan 21, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the closed form of the following power series
    1+3x+6x^2+10x^3+15x^4+21x^5+...

    2. Relevant equations
    1+x+x^2+.. = 1/(1-x)


    3. The attempt at a solution
    I tried differentiating but couldn't get it to any expression that I know the sum for.. I was playing around trying to find some kind of increasing arithmetic sum but couldn't figure out how to get the closed form
     
  2. jcsd
  3. Jan 21, 2009 #2

    Dick

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    Take 1+x+x^2+... = 1/(1-x) and differentiate both sides. Now do it again. Are you seeing anything useful in the second derivative?
     
  4. Jan 21, 2009 #3
    Great, got it thanks:)
     
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