1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook