(adsbygoogle = window.adsbygoogle || []).push({}); 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]

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# Homework Help: Sum of Series.

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