- #1

student45

[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.