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Homework Help: Sum of Series.

  1. Nov 8, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the sum of the following series

    [tex]\sum_{n=1}^{\infty}n(n+1)x^n[/tex]


    3. The attempt at a solution


    [tex]x\sum_{n=1}^{\infty}n(n+1)x^{n-1}[/tex]

    [tex]x\int_{0}^{x}(\int_{0}^{x}f(t)dt)dt=x(x^2+x^3+x^4+x^5+\cdots)=x\frac{x^2}{1-x}[/tex]


    [tex]x\frac{d^2}{dx^2}\frac{x^2}{1-x}=\frac{2x}{1-x}[/tex]
     
  2. jcsd
  3. Nov 8, 2007 #2
    I am not really sure of how to do this but looking at your last line, I think you messed up taking the second derivative of x^2/(1-x) since you need to use the quotient rule, the (1-x) should be squared on each derivative
     
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