I'm trying to find the sum of this: [tex] \[ \sum\limits_{n = 0}^\infty {( - 1)^n nx^n } \] [/tex] This is what I have so far: [tex] \[ \begin{array}{l} \frac{1}{{1 - x}} = \sum\limits_{n = 0}^\infty {x^n } \\ \frac{1}{{(1 - x)^2 }} = \sum\limits_{n = 0}^\infty {nx^{n - 1} } = \sum\limits_{n = 1}^\infty {nx^{n - 1} } \\ \frac{x}{{(1 - x)^2 }} = \sum\limits_{n = 1}^\infty {nx^n } \\ \end{array} \] [/tex] So how do I get the (-1)^n part in there? Any suggestions would be really helpful. Thanks.